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Part of 1987 Austrian-Polish Competition

Problems(1)

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

Source: Austrian Polish 1987 APMC

4/30/2020
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.
polynomialalgebraprime divisors