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Polynomial with a constructor sequence

Source: BdMO 2024 Higher Secondary National P6

March 18, 2024

algebrapolynomialSubstitution

Problem Statement

Find all polynomials

P(x)

for which there exists a sequence

a_1, a_2, a_3, \ldots

of real numbers such that

a_m + a_n = P(mn)

for any positive integer

m

and

n

.

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