Problem

Source: IMO Shortlist 1989, Problem 15, ILL 50

Tags: number theory, system of equations, Diophantine equation, Additive Number Theory, IMO Shortlist



Let a,b,c,d,m,nZ+ such that a2+b2+c2+d2=1989, a+b+c+d=m2, and the largest of a,b,c,d is n2. Determine, with proof, the values of m and n.