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(1 + 2x)P(2x) = (1 + 2^{1999}x)P(x) .

Source: VI Soros Olympiad 1990-00 R2 11.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 28, 2024
algebrapolynomial

Problem Statement

Find all polynomials P(x)P(x) with real coefficients such that for all real xx holds the equality (1+2x)P(2x)=(1+21999x)P(x).(1 + 2x)P(2x) = (1 + 2^{1999}x)P(x) .
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