MathDB

18

Part of 2023 Baltic Way

Problems(1)

Combi NT

Source: Baltic Way 2023/18

11/11/2023
Let p>7p>7 be a prime and let AA be subset of {0,1,…,p−1}\{0,1, \ldots, p-1\} with size at least p−12\frac{p-1}{2}. Show that for each integer rr, there exist a,b,c,d∈Aa, b, c, d \in A, not necessarily distinct, such that ab−cd≡r(modp)ab-cd \equiv r \pmod p.
number theory