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2013 EGMO
4
4
Part of
2013 EGMO
Problems
(1)
P(n) takes integer values at three consecutive integers
Source: European Girl's MO 2013, Problem 4
4/11/2013
Find all positive integers
a
a
a
and
b
b
b
for which there are three consecutive integers at which the polynomial
P
(
n
)
=
n
5
+
a
b
P(n) = \frac{n^5+a}{b}
P
(
n
)
=
b
n
5
+
a
takes integer values.
algebra
polynomial
number theory
EGMO