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Determine all values of a^2+b^2+c^2+d^2 for primes a,b,c,d

Source: Baltic Way 1999

December 23, 2010
number theoryprime numbersnumber theory proposed

Problem Statement

Let a,b,ca,b,c and dd be prime numbers such that a>3b>6c>12da>3b>6c>12d and a2−b2+c2−d2=1749a^2-b^2+c^2-d^2=1749. Determine all possible values of a2+b2+c2+d2a^2+b^2+c^2+d^2 .
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