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P(x) = x^n - 1987x, rational x,y with P(x) = P(y) , then x = y

Source: Austrian Polish 1987 APMC

April 30, 2020
polynomialalgebraprime divisors

Problem Statement

Let nn be the square of an integer whose each prime divisor has an even number of decimal digits. Consider P(x)=xnāˆ’1987xP(x) = x^n - 1987x. Show that if x,yx,y are rational numbers with P(x)=P(y)P(x) = P(y), then x=yx = y.
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