Find all (a,b) s.t. a|b^2, b|a^2, a+1 | b^2 + 1
Source: Serbian National Olympiad 2012, Problem 2
April 4, 2012
number theorygreatest common divisoralgebrapolynomialVietainequalitiesnumber theory proposed
Problem Statement
Find all natural numbers and such that a|b^2, b|a^2 \mbox{ and } a+1|b^2+1.