Cauchy-Davenport Theorem

Explanations 5

• The well known result ∣A+B∣≥∣A∣+∣B∣−1|A+B| \ge |A|+|B|-1∣A+B∣≥∣A∣+∣B∣−1 in the reals is also true modulo ppp (at least when ppp is prime), and it is called the Cauchy Davenport …

  By Ryan Alweiss, Victor Wang, Victor Wang

• (Erdos-Ginsburg-Ziv, or EGZ) Prove that among any 2n−12n-12n−1 integers, where nnn is a positive integer, there exist nnn who sum to a multiple of nnn.

  By Ryan Alweiss

• (2013 TSTST 5) Let ppp be a prime. Prove that any complete graph with 1000p1000p1000p vertices, whose edges are labelled with integers, has a cycle whose sum of labels is divisi…

  By Ryan Alweiss

• (2007 ISL N3) Let XXX be a set of 10,000 integers, none of them is divisible by 47. Prove that there exists a 2007-element subset YYY of XXX such that a−b+c−d+ea -b + c - d + ea…

  By Franklyn Wang

• Let ppp be a prime and ddd be a factor of p−1p-1p−1. Prove that for every integer nnn, there exist integers a1,a2,...,ada_1,a_2,...,a_da1​,a2​,...,ad​ such that a1d+a2d+...+add≡…

  By Toan Pham