MathDB

N4

Part of 2014 Indonesia MO Shortlist

Problems(1)

Exactly one solution

Source: Indonesian Mathematical Olympiad 2014 Day 1 Problem 2

9/3/2014
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.
calculusintegrationnumber theory unsolvednumber theory