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Putnam 1952 A1

  • Session A
  1. Let f(x)=∑i=0i=naixn−if(x)=\sum_{i=0}^{i=n} a_{i} x^{n-i} be a polynomial of degree nn with integral coefficients. If a0,ana_{0}, a_{n}, and f(1)f(1) are odd, prove that f(x)=0f(x)=0 has no rational roots.

Dataset text PutnamGAP. Quoted with source.

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