MathDB

13

Part of 1983 IMO Longlists

Problems(1)

Prove that a_i and a_j exist for every prime p

Source:

10/5/2010
Let pp be a prime number and a1,a2,…,a(p+1)/2a_1, a_2, \ldots, a_{(p+1)/2} different natural numbers less than or equal to p.p. Prove that for each natural number rr less than or equal to pp, there exist two numbers (perhaps equal) aia_i and aja_j such that p≡aiaj(modr).p \equiv a_i a_j \pmod r.
modular arithmeticnumber theory proposednumber theory