MathDB

14

Part of 2019 Latvia Baltic Way TST

Problems(1)

Existence of integer satisfying divisibility condition

Source: Latvian TST for Baltic Way 2019 Problem 14

5/29/2020
Let mm be a positive integer and pp be a prime, such that m2−2m^2 - 2 is divisible by pp. Suppose that there exists positive integer aa such that a2+m−2a^2+m-2 is divisible by pp. Prove that there exists positive integer bb such that b2−m−2b^2- m -2 is divisible by pp.
number theory unsolvednumber theory