Zhi-Wei Sun's Papers

Zhi-Wei Sun's Papers Classified by Field

A. Disjoint Residue Classes
A1. On disjoint residue classes, 　　 Discrete Math., 104(1992), no.3, 321--326. 　　 MR 93d:11005; Zbl. M. 755.11002. A2. Solutions to two problems of Huhn and Megyesi (Chinese), 　　 Chinese Ann. Math. Ser. A, 13(1992), no.6, 722--727. 　　 MR 94c:11001; Zbl. M. 770.11003.

B. Covers of the Integers by Residue Classes
B1. Some results on covering systems of congruences (Chinese, English abstract) (with Z. H. Sun), 　　 J. Southwest-China Teachers Univ., 1987, no.1, 10--15. 　　 Zbl. M. 749.11018. B2. A theorem concerning systems of residue classes, 　　 Acta Math. Univ. Comenian. (N. S.), 60(1991), no.1, 123--131. 　　 MR 92f:11007; Zbl. M. 734.11022. B3. An improvement to the Zn\'am-Newman result (Chinese, English abstract), 　　 Chinese Quart. J. Math., 6(1991), no.3, 90--96. B4. On covering systems with distinct moduli (Chinese, English abstract), 　　 J. Yangzhou Teachers College (Nat. Sci. Ed.), 11(1991), no.3, 21--27. B5. On exactly m times covers, 　　 Israel J. Math., 77(1992), no.3, 345--348. 　　 MR 93k:11007; Zbl. M. 768.11001. B6. Covering the integers by arithmetic sequences, 　　 Acta Arith., 72( 1995), no.2, 109--129. 　　 MR 96k:11013; Zbl. M. 841.11011. B7. Covering the integers by arithmetic sequences II, 　　 Trans. Amer. Math. Soc., 348(1996), no.11, 4279--4320. 　　 MR 97c:11011; Zbl. M. 884.11013. B8. Exact m-covers and the linear form $\sum^k_{s=1}x_s/n_s$, 　　 Acta Arith., 81(1997), no.2, 175--198. 　　 MR 98h:11019; Zbl. M. 871.11011. B9. Covers with less than 10 moduli and their applications (with S.-M. Yang), 　　 J. Southeast Univ. (English Edition), 14(1998), no.2, 106--114. 　　 MR 2000i:11157. Zbl. M. 1008.11003. B10.On covering multiplicity, 　　 Proc. Amer. Math. Soc., 127(1999), no.5, 1293--1300. 　　 MR 99h:11012; Zbl. M. 917.11006. B11.On n-dimensional covering systems (Chinese) (with Z. Hu), 　　 Nanjing Univ. J. Natur. Sci., 37(2001), no.4, 486--492. MR 2002j;11006; Zbl. M. 1035.11005. B12.On the function $w(x)=\|{1\le s\le k: x \equiv a_s (mod n_s)}\|$, 　　 Combinatorica, 23(2003), no.4, 681--691. MR 2004m:11013; Zbl. M. 1047.11014. B13.On m-covers and m-systems, submitted, arXiv:math.NT/0403271. B14.On the range of a covering function, 　　 J. Number Theory 111(2005), no.1, 190--196. MR 2005m:11015. B15.On odd covering systems with distinct moduli (with S. Guo), 　　 Adv. in Appl. Math. 35(2005), no.2, 182--187. B16.On covering numbers, 　　 INTEGERS: Electron. J. Combin. Number Theory 7(2007), no.2, #A33, 11pp (electronic). B17.A connection between covers of the integers and unit fractions, 　　 Adv. in Appl. Math. 38(2007), no.2, 267--274. B18.A sharp result on m-covers (with H. Pan), 　　 Proc. Amer. Math. Soc. 135(2007), no.11, 3515--3520. B19. Covers of the integers with odd moduli and their applications to the forms $x^m-2^n$ and $x^2-F_{3n}/2$ (with. K. J. Wu), 　　 Math. Comp. 78(2009), no.267, 1853--1866. B20. On m-covers and m-systems, 　　 Bull. Austral. Math. Soc., to appear. arXiv:math.NT/0403271.

C. Covers of Groups by Cosets or Subgroups
C1. Finite coverings of groups, 　　 Fund. Math., 134(1990), no.1, 37--53. 　　 MR 91g:20031; Zbl. M. 717.20020. C2. Exact m-covers of groups by cosets, 　　 European J. Combin., 22(2001), no.3, 415--429. MR 2002a:20026; Zbl. M. 0980.20032. C3. On the Herzog-Sch\"onheim conjecture for uniform covers of groups (Abstract), 　　 J. Algebra 273(2004), no.1, 153--175. MR 2005d:20074; Zbl. M. 1067.20057. C4. Finite covers of groups by cosets or subgroups, 　　 Internat. J. Math. 17(2006), no.1, 1047--1064. C5. On covers of abelian groups by cosets (with G. Lettl), 　　 Acta Arith. 131(2008), no.4, 341-350.

D. Diophantine Equations
D1. A necessary and sufficient condition for two linear diophantine equations 　　 to have a common solution (Chinese, English abstract), 　　 Nanjing Univ. J. Natur. Sci., 25(1989), no.1, 10--17. 　　 MR 90i:11026; Zbl. M. 686.10009. D2. On integers not of the form $\pm p^a\pm q^b$, 　　 Proc. Amer. Math. Soc., 128(2000), no.4, 997--1002. 　　 MR 2000i:11157; Zbl. M. 959.11043. D3. Integers not of the form $c(2^a+2^b)+p^{\alpha}$ (with M.-H. Le), 　　 Acta Arith., 99(2001), no.2, 183--190. MR 2002e:11043; Zbl. M. 1006.11015. D4. A note on integers of the form $2^n+cp$ (with S. M. Yang), 　　 Proc. Edinburgh Math. Soc., 45(2002), no.1, 155--160. MR 2002j:11117. D5. On systems of linear diophantine equations and linear congruences 　　 (Chinese, English summary) (with H. Pan), 　　 Nanjing Univ. J. Math. Biquarterly, 19(2002), no.1, 61--67. MR 2003d:11037.

E. Covering Equivalence and Periodic Arithmetical Maps
E1. Several results on systems of residue classes, 　　 Adv. Math. (China), 18(1989), no.2, 251--252. E2. Systems of congruences with multipliers (Chinese, English abstract), 　　 Nanjing Univ. J. Math. Biquarterly, 6(1989), no.1, 124--133. 　　 MR 90m:11006; Zbl. M. 703.11002. E3. On a generalization of a conjecture of Erd\"os, 　　 Nanjing Univ. J. Natur. Sci., 27(1991), no.1, 8--15. 　　 MR 92f:11008; Zbl. M. 805.11017. E4. Algebraic approaches to periodic arithmetical maps, 　　 J. Algebra, 240(2001), no.2, 723--743. MR 2002f:11009; Zbl. M. 0974.11007. E5. On covering equivalence, 　　 in: `Analytic Number Theory' (Beijing/Kyoto, 1999), 277--302, 　　 Dev. Math., 6, Kluwer Acad. Publ., Dordrecht, 2002. MR 2003g:11014; Zbl. M. 1026.11020. E6. Arithmetic properties of periodic maps, 　　 Math. Res. Lett. 11(2004), no.2, 187--196. MR 2005g:11015. E7. A reciprocity law for uniform functions, 　　 Nanjing Univ. J. Math. Biquarterly 21(2004), no.2, 201--205. MR 2006a:11004; Zbl. M. 1066.11003. E8. Two local-global results in combinatorial number theory (Chinese), 　　 Bull. Chinese Math. Soc. 2005, no.4, 13--17. E9. A local-global theorem on periodic maps, 　　 J. Algebra 293(2005), no.2, 506--512. E10.A characterization of covering equivalence (with H. Pan), 　　 Acta Arith. 129(2007), no.4, 397--402.

F. Bernoulli Polynomials and Euler Polynomials
F1. Values of Bernoulli polynomials (with A. Granville), 　　 Pacific J. Math., 172(1996), no.1, 117--137. 　　 MR 98b:11018; Zbl. M. 856.11008. F2. General congruences for Bernoulli polynomials, 　　 Discrete Math., 262(2003), 253--276. MR 2003m:11037. 　　 [Ranked 12th among the top 25 of the most downloaded articles (from Jan. to May 2003).] F3. Some identities for Bernoulli and Euler polynomials (with K. J. Wu and H. Pan), 　　 Fibonacci Quart., 42(2004), no.4, 295-299. MR 2006a:11024; Zbl. M. 1064.11019. F4. On Euler numbers modulo powers of two, 　　 J. Number Theory 115(2005), no.2, 371--380. F5. Explicit congruences for Euler polynomials, 　　 Number Theory: Tradition and Modernization, Springer, 2006, pp. 205-218. F6. New identities involving Bernoulli and Euler polynomials (with H. Pan), 　　 J. Combin. Theory Ser. A 113(2006), no.1, 156--175. 　　 Original version: arXiv:math.NT/0407363 and arXiv:math.NT/0408223. F7. On q-Euler numbers, q-Sali\'e numbers and q-Carlitz numbers (with H. Pan), 　　 Acta Arith. 124(2006), no.1, 41--57. F8. Identities concerning Bernoulli and Euler polynomials, 　　 Acta Arith. 125(2006), no.1, 21--39. F9. Symmetric identities for Euler polynomials (with Y. Zhang and H. Pan), 　　 preprint, arXiv:0812.0962.

G. Binomial Coefficients and Combinatorial Congruences
G1. A congruence for primes, 　　 Proc. Amer. Math. Soc., 123(1995), no.5, 1341--1346. 　　 MR 95f:11003; Zbl. M. 833.11001. G2. Products of binomial coefficients modulo $p^2$, 　　 Acta Arith., 97(2001), no.1, 87--98. MR 2002m:11013; Zbl. M. 986.11009. G3. A curious identity involving binomial coefficients, 　　 Integers: Electronic J. Combin. Number Theory, 2(2002), A04, 8 pp. 　　 MR 2003b:05018; Zbl. M. 0986.05012. G4. On the sum $\sum_{k\equiv r (mod m)}\binom {n}{k}$ and related congruences, 　　 Israel J. Math., 128(2002), 135--156. MR 2003d:11026. G5. Combinatorial identities in dual sequences, 　　 European J. Combin., 24(2003), no.6, 709--718. MR 2004g:05017; Zbl. M. 1024.05010. G6. A combinatorial identity with application to Catalan numbers (with H. Pan), 　　 Discrete Math. 306(2006), no.16, 1921--1940. G7. An extension of a curious binomial identity (with K. J. Wu), 　　 Int. J. Mod. Math. 2(2007), no.2, 247--251. G8. Congruences for sums of binomial coefficients (with R. Tauraso), 　　 J. Number Theory 126(2007), no.2, 287--296. 　　 [Ranked 1st among the most downloaded articles during July.-Sept. in 2007] G9. On sums of binomial coefficients and their applications, 　　 Discrete Math. 308(2008), no.18, 4231--4245. G10. Some congruences for the second order Catalan numbers (with L. L. Zhao and H. Pan), 　　 Proc. Amer. Math. Soc. 138(2010), no.1, 37--46. G11. On some new congruences for binomial coefficients (with R. Tauraso), 　　 Acta Arith., revised. arXiv:0709.1665. G12.New congruences for central binomial coefficients (with R. Tauraso), 　　 Adv. in Appl. Math., to appear. arXiv:0805.0563. G13. Some curious congruences modulo primes (with L.-L. Zhao), 　　 J. Number Theory, to appear. arXiv:0904.1162. G14. Various congruences involving binomial coefficients and higher-order Catalan numbers , 　　 preprint, arXiv:0909.3808. G15. Binomial coefficients, Catalan numbers and Lucas quotients, 　　 preprint, arXiv:0909.5648. G16. On sums of binomial coefficients modulo p^2, 　　 preprint, arXiv:0910.5667. G17. On congruences related to central binomial coefficients, 　　 preprint, arXiv:0911.2415. G18. Binomial coefficients, Catalan numbers and Lucas quotients (II), 　　 preprint, arXiv:0911.3060. G19. Arithmetic theory of harmonic numbers, 　　 preprint, arXiv:0911.4433. G20. Congruences involving binomial coefficients and Lucas sequences, 　　 preprint, arXiv:0912.1280. G21. Curious congruences for Fibonacci numbers, 　　 preprint, arXiv:0912.2671. G22. Super congruences and Euler numbers, 　　 preprint, arXiv:1001.4453.

H. p-adic Methods and Applications
H1. Polynomial extension of Fleck's congruence, 　　 Acta Arith. 122(2006), no.1, 91--100. H2. A number-theoretic approach to homotopy exponents of SU(n) (with D. M. Davis), 　　 J. Pure Appl. Algebra 209(2007), no.1, 57--69. H3. Combinatorial congruences modulo prime powers (with D. M. Davis), 　　 Trans. Amer. Math. Soc. 359(2007), no.11, 5525--5553. H4. Combinatorial congruences and Stirling numbers, 　　 Acta Arith. 126(2007), no.4, 387--398. H5. On Fleck quotients (with D. Wan), 　　 Acta Arith. 127(2007), no.4, 337--363. H6. Lucas-type congruences for cyclotomic $\psi$-coefficients (with D. Wan), 　　 Int. J. Number Theory 4(2008), no. 2, 155--170. H7. Binomial coefficients and the ring of p-adic integers (with W. Zhang), 　　 preprint, arXiv:0812.3089. H8. Extensions of Wilson's lemma and the Ax-Katz theorem, 　　 preprint, arXiv:math.NT/0608560. H9. Fleck quotients and Bernoulli numbers, 　　 submitted, arXiv:math.NT/0608328. H10.On 2-adic orders of some binomial sums (with H. Pan), 　　 preprint, arXiv:0909.4945. H11.p-adic valuations of some sums of multinomial coefficients, 　　 preprint, arXiv:0910.3892. H12.Some q-congruences related to 3-adic valuations (with H. Pan), 　　 preprint, arXiv:0910.4170.

I. Restricted Sumsets and Zero-sum Problems
I1. On sums of distinct representatives (with H.-Q. Cao), 　　 Acta Arith., 87(1998), no.2, 159--169. 　　 MR 99k:11021; Zbl. M. 920.11010. I2. A note on the Erd\"os-Ginzburg-Ziv theorem (with J.-X. Liu), 　　 Nanjing Univ. J. Natur. Sci., 37(2001), no.4, 473--476. MR 2002j:11014. I3. Restricted sums of subsets of $\Bbb Z$, 　　 Acta Arith., 99(2001), no.1, 41--60. MR 2002j:11016; Zbl. M. 0974.11009. I4. Hall's theorem revisited, 　　 Proc. Amer. Math. Soc., 129(2001), no.10, 3129--3131. MR 2002h:05007; Zbl. M. 0966.05067. I5. Restricted sums in a field (with Q. H. Hou), 　　 Acta Arith., 102(2002), no.3, 239--249. MR 2003e:11025; Zbl. M. 0988.11008. I6. Sums of subsets with polynomial restrictions (with J. X. Liu), 　　 J. Number Theory, 97(2002), no.2, 301--304. MR 2004c:11027; Zbl. M. 1034.11021. I7. A lower bound for $\|{a+b: a\in A, b\in B, P(a,b)\not=0}\|$ (with H. Pan), 　　 J. Combin. Theory Ser. A, 100(2002), no.2, 387--393. MR 2003k:11016; Zbl. M. 1020.11080. I8. Unification of zero-sum problems, subset sums and covers of Z (Research Announcement), 　　 Electron. Res. Announc. Amer. Math. Soc., 9(2003), 51--60. MR 2004i:11017; Zbl. M. 1062.11015. 　　 [Submitted on 2003-03-20 and communicated by R. L. Graham.] I9. On Snevily's conjecture and restricted sumsets, 　　 J. Combin. Theory Ser. A, 103(2003), no.2, 291--304. MR 2004k:11026; Zbl. M. 1042.11016. I10.On various restricted sumsets (with Y. N. Yeh), 　　 J. Number Theory 114(2005), no.2, 209--220, I11.Restricted sumsets and a conjecture of Lev (with H. Pan), 　　 Israel J. Math. 154(2006), no.1, 21--28. I12.On the number of zero-sum subsequences (with H.-Q. Cao), 　　 Discrete Math. 307(2007), no.13, 1687--1691. I13. A survey of problems and results on restricted sumsets, 　　 in: Number Theory (edited by S. Kanemitsu and J.-Y. Liu), World Sci., Singapore, 2007, 190--213. I14.On value sets of polynomials over a field, 　　 Finite Fields Appl. 14(2008), no.2, 470-481. I15.An additive theorem and restricted sumsets, 　　 Math. Res. Lett. 15(2008), no.6, 1263-1276. I16.A variant of Tao's method with application to restricted sumsets (with S. Guo), 　　 J. Number Theory 129(2009), no.2, 434-438. I17.Zero-sum problems for abelian p-groups and covers of the integers by residue classes, 　　 Israel J. Math. 170(2009), 235-252. I18.On Bialostocki's conjecture for zero-sum sequences (with S. Guo), 　　 Acta Arith., 140(2009), no.4, 329--334. I19.A new extension of the Erdos-Heilbronn conjecture (with H. Pan), 　　 J. Combin. Theory Ser. A 116(2009), no.8, 1374--1381. I20.Exterior algebras and two conjectures on finite abelian groups (with T. Feng and Q. Xiang), 　　 Israel J. Math., to appear. arXiv:0808.2753. I21.Linear extension of the Erdos-Heilbronn conjecture (with Lilu Zhao), 　　 preprint, arXiv:0810.0467.

J. Dedekind Sums and Related Sums
J1. Sums of minima and maxima, 　　 Discrete Math., 257(2002), no.1, 143--159. 　　 MR 2003g:11037; Zbl. M. 1007.05018 J2. Generalizations of Knopp's identity (with B. F. Chen), 　　 J. Number Theory, 97(2002), no.1, 186--198. 　　 MR 2003i:11054; Zbl. M. 1033.11017.

K. Linear Recurrences
K1. Fibonacci numbers and Fermat's last theorem (with Z. H. Sun), 　　 Acta Arith., 60(1992), no.4, 371--388. 　　 MR 93e:11025; Zbl. M. 725.11009, 739.11004. K2. Some identities on linear recurrent sequences of second order 　　 (Chinese, English abstract) (with H. Hu), 　　 Nanjing Univ. J. Math. Biquarterly, 17(2000), no.1, 86--92. 　　 MR 2001e:11012; Zbl. M. 1020.11013. K3. Reciprocal sums of second-order recurrent sequences (with H. Hu and J.-X. Liu), 　　 Fibonacci Quart., 39(2001), no.3, 214--220. MR 2002d:11016; Zbl. M. 0992.11014. K4. An extension of Lucas' theorem (with H. Hu), 　　 Proc. Amer. Math. Soc., 129(2001), no.12, 3471--3478. MR 2002i:11019. K5. On harmonic numbers and Lucas sequences, 　　 preprint, arXiv:1001.0348.

L. Quadratic Fields, Power Residues, and Representations of Integers
L1. Binomial coefficients and quadratic fields, 　　 Proc. Amer. Math. Soc. 134(2006), no.8, 2213--2222. L2. Simple arguments on consecutive power residues, 　　 J. Number Theory 124(2007), no.1, 57--61. L3. Mixed sums of squares and triangular numbers, 　　 Acta Arith. 127(2007), no.2, 103--113. L4. Mixed sums of squares and triangular numbers (II) (with S. Guo and H. Pan), 　　 Integers: Electron. J. Combin. Theory, 7(2007), #A56, 5 pp.(electronic) L5. On sums of primes and triangular numbers, 　　 Journal of Combinatorics and Number Theory 1(2009), no.1, 65--76. arXiv:0803.3737. L6. Mixed sums of squares and triangular number (III) (with B. K. Oh), 　　 J. Number Theory 129(2009), no.4, 964-969. L7. On almost universal mixed sums of squares and triangular numbers (with B. Kane), 　　 Trans. Amer. Math. Soc., accepted. arXiv:0808.2761. L8. Mixed sums of primes and other terms, 　　 in: Additive Number Theory (edited by D. Chudnovsky and G. Chudnovsky), Springer, to appear. arXiv:0901.3075. L9. On universal sums of polygonal numbers, 　　 preprint, arXiv:0905.0635. L10.On some universal sums of generalized polygonal numbers (with F. Ge), 　　 preprint, arXiv:0906.2450.

M. Diophantine Representations
M1. Some diophantine representations related to $\binom{PX}{QX}$ (Chinese, English abstract), 　　 in: Selected Papers on BCI and BCK Algebras and Computer Logics (edited by B.-Y. Shen), 　　 Shanghai Jiaotong Univ. Press, Shanghai, 1991, 131--138. M2. Reduction of unknowns in Diophantine representations, 　　 Sci. China Ser. A, 35(1992), no.3, 257--269. 　　 Chinese Edition, 1991, no.10, 1030--1040. 　　 MR 93h:11039; Zbl. M. 773.11077. M3. Singlefold Diophantine representation of the sequence 　　 $u_0=0, u_1=1$ and $u_{n+2}=mu_{n+1}+u_n$, 　　 in: Pure and Applied Logic (edited by J.-W. Zhang), 　　 Beijing Univ. Press, Beijing, 1992, 97--101. M4. A new relation-combining theorem and its application, 　　 Z. Math. Logik Grundlag. Math., 38(1992), no.3, 209--212. 　　 MR 94m:03069; Zbl. M. 793.03004. M5. Further results on Hilbert's temth problem, 　　 Ph.D. Thesis, Nanjing University, Nanjing, 1992. M6. Jone's work on Hilbert's tenth problem and related topics (Chinese, English abstract), 　　 Adv. Math. (China), 22(1993), no.4, 312--331. 　　 MR 94j:03089; Zbl. M. 791.03005.

N. Combinatorics
N1. On the unique representability of spikes over prime fields (with Z. Y. Wu), 　　 Discrete Math. 306(2006), no.15, 1798--1804. N2. Determination of the two-color Rado number for a_1x_1+...+a_mx_m=x_0 (with S. Guo), 　　 J. Combin. Theory Ser. A, 115(2008), no.2, 345--353. N3. Groups in combinatorial number theory, 　　 in: Proceedings of the 4th International Congress of Chinese Mathematicians (Hangzhou, 2007), 　　 Vol. I, Higher Education Press, Beijing, 2007, pp. 475--495.

O. Logic and Computer Science
O1. Some results on recursive functions (Chinese, English abstract), 　　 Nanjing Univ. J. Math. Biquarterly, 4(1987), no.2, 196--206. 　　 Zbl. M. 657.03022. O2. Definition of degree of unsolvablity on real numbers (with X. Z. Zheng and D. C. Ding), 　　 Chinese Sci. Bull. (Chinese Edition), 38(1993), no.3, 203--206. O3. Equivalent propositions about $R$-reconstructions in open logic (with K. L. Su), 　　 Nanjing Univ. J. Math. Biquarterly, 11(1994), no.1, 6--9. 　　 MR 95k:68219; Zbl. M. 808.03012. O4. Fixed points of a class of operators in open logic (with K. L. Su, D. C. Ding and L. Qian), 　　 Acta Sci. Natur. Univ. Norm. Hunan., 17(1994), no.3, 21--23. 　　 MR 96c:68189; Zbl. M. 816.03014. O5. Class of models for a rejection by reasonal facts (with K. L. Su, D. C. Ding and L. Qian), 　　 Chinese J. Comput., 17(1994), no.5, 361--366. O6. Reconstructions and epistemic processes in the open logic system 　　 (with K. L. Su, D. C. Ding and L. Qian), 　　 in: Proc. of the National Confer. on the Fundamental Theories of Artificial Intelligence, 　　 Tsinghua Univ. Press, Beijing, 1994, pp. 163--168. O7. The continuum Hypothesis and Turing degrees (with K. L. Su and D. C. Ding), 　　 Acta Math. Sinica, 39(1996), no.1, 71--75. 　　 MR 97e:03064; Zbl. M. 863.03023. O8. On the emptiness problem for two-way NFA with one reversal-bounded counter 　　 (with Z. Dang and O. H. Ibarra), 　　 in: P. Bose and P. Morin (Eds.), Algorithms and Computation, 　　 Lecture Notes in Computer Science, Vol. 2518, Springer, 2002, pp. 103--114. O9. Safety verification for two-way finite automata with monotonic counters 　　 (with O. H. Ibarra and Z. Dang), 　　 in: M. Ito and M. Toyama (Eds.), Developments in Language Theory 2002, 　　 Lecture Notes in Computer Science, Vol. 2450, Springer, 2003, pp. 326--338. Zbl. M. 1015.68112. O10.On two-way nondeterministic finite automata with 　　 one reversal-bounded counter (with Z. Dang and O. Ibarra), 　　 Theoret. Comput. Sci. 330(2005), no.1, 59--79. MR 2005h:68068.


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