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PutnamSuperchallengeIntegrals I: Feynman's Trick

Integrals I: Feynman's Trick · Superchallenge problem

Compute the determinant of the 5×55\times5 circulant matrix whose first row is (3,4,7,3,5)(3, 4, 7, 3, 5) and whose each later row is the previous one shifted right by one.