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2016 Canada National Olympiad
3
Polynomial Prime Values
Polynomial Prime Values
Source: 2016 CMO #3
April 10, 2016
algebra
polynomial
number theory
Problem Statement
Find all polynomials
P
(
x
)
P(x)
P
(
x
)
with integer coefficients such that
P
(
P
(
n
)
+
n
)
P(P(n) + n)
P
(
P
(
n
)
+
n
)
is a prime number for infinitely many integers
n
n
n
.
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