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International Contests
Tournament Of Towns
1987 Tournament Of Towns
(144) 1
(144) 1
Part of
1987 Tournament Of Towns
Problems
(1)
TOT 144 1987 Spring Main S1 p(a) - p(b) = 1 , integer polynomial
Source:
4/17/2020
Suppose
p
(
x
)
p(x)
p
(
x
)
is a polynomial with integer coefficients. It is known that
p
(
a
)
ā
p
(
b
)
=
1
p(a) - p(b) = 1
p
(
a
)
ā
p
(
b
)
=
1
(where
a
a
a
and
b
b
b
are integers). Prove that
a
a
a
and
b
b
b
differ by
1
1
1
. (Folklore)
polynomial
algebra
Integer Polynomial