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2 roots of x^5-px-1 = 0, are roots of x^2-ax+b= 0$ for some integers a,b

Source: Spanish Mathematical Olympiad 1985 P7

August 2, 2018

polynomialrootsInteger Polynomialpolynomial equationalgebra

Problem Statement

Find the values of

p

for which the equation

x^5 - px-1 = 0

has two roots

r

and

s

which are the roots of equation

x^2-ax+b= 0

for some integers

a,b