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Problem 8 of Third round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022
number theorymodulo

Problem Statement

Determine the number of ordered quadruples of integers (a,b,c,d)(a,b,c,d) for which 0≤a,b,c,d≤360\leq a,b,c,d\leq 36 and 37∣a2+b2−c3−d337|a^2+b^2-c^3-d^3.
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