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(1 + x)(1 + x^2) (1 + x^4) ...(1 + x^{2^k}) = 1 + x + x^2 + x^3+ .. x^m

Source: Polish MO Finals 1958 p4

August 29, 2024
algebra

Problem Statement

Prove that if k k is a natural number, then (1+x)(1+x2)(1+x4)…(1+x2k)=1+x+x2+x3+…+xm (1 + x)(1 + x^2) (1 + x^4) \ldots (1 + x^{2^k}) =1 + x + x^2 + x^3+ \ldots + x^m where m m is a natural number dependent on k k ; determine m m .
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