olymmath

ISL 2018 N5

    Four positive integers x,y,zx, y, z, and tt satisfy the relations xy−zt=x+y=z+t.x y-z t=x+y=z+t . Is it possible that both xyx y and ztz t are perfect squares? (Russia)

    Dataset text NuminaMath olympiads. Quoted with source.

    Official text: IMO 2018 Shortlist booklet, page 9.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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