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APMO
2018 APMO
5
5
Part of
2018 APMO
Problems
(1)
P(s) and P(t) integers implies P(st) integer
Source: APMO 2018 P5
6/24/2018
Find all polynomials
P
(
x
)
P(x)
P
(
x
)
with integer coefficients such that for all real numbers
s
s
s
and
t
t
t
, if
P
(
s
)
P(s)
P
(
s
)
and
P
(
t
)
P(t)
P
(
t
)
are both integers, then
P
(
s
t
)
P(st)
P
(
s
t
)
is also an integer.
Polynomials
algebra
APMO
number theory