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f (x) = x^n + x^{n-1} +...+ x + 1= g (h (x))

Source: 15th -b QEDMO problem 5 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

May 30, 2021
algebrapolynomial

Problem Statement

For which natural numbers nn can the polynomial f(x)=xn+xnāˆ’1+...+x+1f (x) = x^n + x^{n-1} +...+ x + 1 as write f(x)=g(h(x))f (x) = g (h (x)), where gg and hh should be real polynomials of degrees greater than 11?
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