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Number TheorySuperchallengeThe Chinese Remainder Theorem

The Chinese Remainder Theorem · Superchallenge problem

Find the sum of all integers xx with 0≤x<17290 \le x < 1729 such that 1729=7⋅13⋅191729 = 7 \cdot 13 \cdot 19 divides x2+x+1x^2 + x + 1.