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    OlympiadHardNumber Theory10–12

    A Difference of Squares Equal to 2025

    Uma Diferença de Quadrados Igual a 2025

    How many pairs of positive integers (x,y)(x, y) satisfy x2−y2=2025x^{2} - y^{2} = 2025?

    Factor the left side and let each factorisation of 20252025 propose a pair; then ask which proposals give positive integers.

    Solution

    Step 1 of 6

    1. 1.x2−y2=(x−y)(x+y)=2025x^{2} - y^{2} = (x - y)(x + y) = 2025.