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The solutions of the equation are integers, no perfect sq.

Source: Balkan MO 1995, Problem 3

April 24, 2006
modular arithmeticnumber theory proposednumber theoryFermat s Little Theorem

Problem Statement

Let aa and bb be natural numbers with a>ba > b and having the same parity. Prove that the solutions of the equation x2−(a2−a+1)(x−b2−1)−(b2+1)2=0 x^2 - (a^2 - a + 1)(x - b^2 - 1) - (b^2 + 1)^2 = 0 are natural numbers, none of which is a perfect square. Albania
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