olymmath

IMO 1977 Problem 5

  • Day 2

Let a,ba,b be two natural numbers. When we divide a2+b2a^2+b^2 by a+ba+b , we the the remainder rr and the quotient q.q. Determine all pairs (a,b)(a, b) for which q2+r=1977.q^2 + r = 1977.

Dataset text AI-MO AoPS. Quoted with source.

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