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Sun Zhiwei

Sun Zhiwei

Conocido Por: Acting

1 Película

Biografía

Born in Huai'an, Jiangsu, Sun and his twin brother Sun Zhihong proved a theorem about what are now known as the Wall–Sun–Sun primes that guided the search for counterexamples to Fermat's last theorem.In 2003, he presented a unified approach to three famous topics of Paul Erdős in combinatorial number theory: covering systems, restricted sumsets, and zero-sum problems or EGZ Theorem.He used q-series to prove that any natural number can be represented as a sum of an even square and two triangular numbers. He conjectured, and proved with B.-K. Oh, that each positive integer can be represented as a sum of a square, an odd square and a triangular number. In 2009, he conjectured that any natural number can be written as the sum of two squares and a pentagonal number, as the sum of a triangular number, an even square and a pentagonal number, and as the sum of a square, a pentagonal number and a hexagonal number.He also raised many open conjectures on congruences and posed over 100 conjectural series for powers of π {\displaystyle \pi } .In 2013, he published a paper containing many conjectures on primes, one of which states that for any positive integer m {\displaystyle m} there are consecutive primes p k , … , p n ( k < n ) {\displaystyle p_{k},\ldots ,p_{n}\ (k<n)} not exceeding 2 m + 2.2 m {\displaystyle 2m+2.2{\sqrt {m}}} such that m = p n − p n − 1 + . . . + ( − 1 ) n − k p k {\displaystyle m=p_{n}-p_{n-1}+...+(-1)^{n-k}p_{k}} , where p j {\displaystyle p_{j}} denotes the j {\displaystyle j} -th prime.In the paper, he refined Lagrange's four-square theorem in various ways and posed many related conjectures one of which is Sun's 1-3-5 conjecture.He is the Editor-in-Chief of the Journal of Combinatorics and Number Theory.

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