MathDB

P={1,2,...,p-1}

Source: Romania TST 1993

August 4, 2009

searchnumber theory unsolvednumber theory

Problem Statement

Let

p\geq 5

be a prime number.Prove that for any partition of the set P\equal{}\{1,2,3,...,p\minus{}1\} in

3

subsets there exists numbers

x,y,z

each belonging to a distinct subset,such that x\plus{}y\equiv z (mod p)