MathDB
M(a, b) = a -1/b +b(b + 3/a) is integer => square also

Source: 2010 Dutch IMO TST2 p3

January 10, 2020
number theoryPerfect Square

Problem Statement

(a) Let aa and bb be positive integers such that M(a,b)=a−1b+b(b+3a)M(a, b) = a - \frac1b +b(b + \frac3a) is an integer. Prove that M(a,b)M(a,b) is a square. (b) Find nonzero integers aa and bb such that M(a,b)M(a,b) is a positive integer, but not a square.
Back to ProblemsView on AoPS