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A5

Part of 1980 Putnam

Problems(1)

Putnam 1980 A5

Source: Putnam 1980

4/1/2022
Let P(t)P(t) be a nonconstant polynomial with real coefficients. Prove that the system of simultaneous equations ∫0xP(t)sin⁡t dt=0,        ∫0xP(t)cos⁡t dt=0 \int_{0}^{x} P(t)\sin t \, dt =0, \;\;\;\; \int_{0}^{x} P(t) \cos t \, dt =0 has only finitely many solutions x.x.
PutnamtrigonometryintegrationpolynomialIndefinite integral