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2013 ToT Fall Senior O p2 P(x) + ax^k, Q(x) + bx^{ell} no common

Source:

March 22, 2020

polynomialalgebra

Problem Statement

Find all positive integers

n

for which the following statement holds: For any two polynomials

P(x)

and

Q(x)

of degree

n

there exist monomials

ax^k

and

bx^{ell}, 0 \le k,\ ell \le n

, such that the graphs of

P(x) + ax^k

and

Q(x) + bx^{ell}

have no common points.