MathDB

15

Part of 1989 IMO Shortlist

Problems(1)

a^2+b^2+c^2+d^2 = 1989

Source: IMO Shortlist 1989, Problem 15, ILL 50

9/18/2008
Let a, b, c, d,m, n \in \mathbb{Z}^\plus{} such that a^2\plus{}b^2\plus{}c^2\plus{}d^2 \equal{} 1989, a\plus{}b\plus{}c\plus{}d \equal{} m^2, and the largest of a,b,c,d a, b, c, d is n2. n^2. Determine, with proof, the values of mm and n. n.
number theorysystem of equationsDiophantine equationAdditive Number TheoryIMO Shortlist