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Nemotron-IMO-Bench 2026 A21

    Let P,Q∈R[X]P,Q\in \mathbb{R}[X] be polynomials of degree not exceeding nn such that P(X)Xn+1+Q(X)(X+1)n+1=1.P(X)X^{n+1}+Q(X)(X+1)^{n+1}=1. What are the possible values of Q(−1/2)Q(-1/2)?

    Dataset text Nemotron-IMO-Bench. Open licence.

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