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TOT 545 1997 Spring S A6 F(x)G(x) = 1 +x + x^2 +...+ x^{n-1}

Source:

September 11, 2024

algebrapolynomial

Problem Statement

Prove that if

F(x)

and

G(x)

are polynomials with coefficients

0

and

1

such that

F(x)G(x) = 1 +x + x^2 +...+ x^{n-1}

holds for some

n > 1

, then one of them can be represented in the form

(1 +x + x^2 +...+ x^{k-1}) T(x)

for some

k > 1

where

T(x)

is a polynomial with coefficients

0

and

1

.
(V Senderov, M Vialiy)

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