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Exactly one solution

Source: Indonesian Mathematical Olympiad 2014 Day 1 Problem 2

September 3, 2014
calculusintegrationnumber theory unsolvednumber theory

Problem Statement

For some positive integers m,nm,n, the system x+y2=mx+y^2 = m and x2+y=nx^2+y = n has exactly one integral solution (x,y)(x,y). Determine all possible values of māˆ’nm-n.
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