MathDB
Problems
Contests
National and Regional Contests
South Africa Contests
South Africa National Olympiad
2017 South Africa National Olympiad
6
6
Part of
2017 South Africa National Olympiad
Problems
(1)
Integer polynomials
Source: SAMO 2017 Q6
7/30/2017
Determine all pairs
(
P
,
d
)
(P, d)
(
P
,
d
)
of a polynomial
P
P
P
with integer coefficients and an integer
d
d
d
such that the equation
P
(
x
)
−
P
(
y
)
=
d
P(x) - P(y) = d
P
(
x
)
−
P
(
y
)
=
d
has infinitely many solutions in integers
x
x
x
and
y
y
y
with
x
≠
y
x \neq y
x
=
y
.
algebra
polynomial
Integer Polynomial
number theory