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Number TheorySuperchallengeHard Number Theory

Hard Number Theory · Superchallenge problem

How many integers aa with 1≤a≤1021 \le a \le 102 are congruent modulo 103103 both to a perfect square and to a perfect cube? (That is, a≡x2a \equiv x^2 and a≡y3(mod103)a \equiv y^3 \pmod{103} for some integers x,yx, y.)