MathDB
f(x) is completely reducible if f (x^{2011}) is also

Source: 10th QEDMO p5 Seniors (8-10. 12. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 16, 2021
polynomialalgebra

Problem Statement

A polynomial f(x)f (x) with real coefficients is called completely reducible if it is a product of at least two non-constant polynomials whose coefficientsare all nonnegative real numbers. Show: If f(x2011)f (x^{2011}) is completely reducible, then f(x)f(x) is also.