2024 Putnam Math Competition - Question A2 - Polynomials with p(p(x)) - x = (p(x) - x)^2 * q(x)
Автор: Nathaniel Johnston
Загружено: 2024-12-12
Просмотров: 970
We solve Problem A2 on the 2024 William Lowell Putnam mathematics competition, which asks: For which real polynomials p is there a real polynomial q such that p(p(x)) - x = (p(x) - x)^2 * q(x)?
PDF content of video: https://njohnston.ca/videos/FJvUDKyQv...
Problem A1 (2024): • 2024 Putnam Math Competition - Question A1...
Problem A6 (2024): • 2024 Putnam Math Competition - Question A6...
Problem B1 (2024): • 2024 Putnam Math Competition - Question B1...
Timestamps:
00:00 Introduction
00:56 Linear polynomials
05:12 Higher-degree polynomials: shifting p
07:45 Expanding the polynomial, using divisibility
11:51 Do it again!
#putnam #mathcompetition #polynomials #functionalequation
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