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Canadian Mathematical Olympiad Qualification Repechage
2015 Canadian Mathematical Olympiad Qualification
2
2
Part of
2015 Canadian Mathematical Olympiad Qualification
Problems
(1)
Tri-divisible polynomial
Source: Canada Repêchage 2015/2
6/18/2016
A polynomial
f
(
x
)
f(x)
f
(
x
)
with integer coefficients is said to be tri-divisible if
3
3
3
divides
f
(
k
)
f(k)
f
(
k
)
for any integer
k
k
k
. Determine necessary and sufficient conditions for a polynomial to be tri-divisible.
polynomial
algebra
number theory