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a+b+c+d=502, a^2-b^2+c^2-d^2=50

Source: Argentina 2005 OMA L3 p1

May 12, 2024
system of equationsnumber theory

Problem Statement

Let a>b>c>da>b>c>d be positive integers satisfying a+b+c+d=502a+b+c+d=502 and a2−b2+c2−d2=502a^2-b^2+c^2-d^2=502 . Calculate how many possible values of a a are there.
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