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Israel Contests
Israel National Olympiad
1998 Israel National Olympiad
6
6
Part of
1998 Israel National Olympiad
Problems
(1)
integer polynomial p(x) with p(7) = 77, p(m) = 0, and p(n) = 85
Source: Israel Joseph Gillis Mathematical Olympiad 1998 p6
2/16/2020
Find all pairs
(
m
,
n
)
(m,n)
(
m
,
n
)
of integers with
m
>
n
>
7
m > n > 7
m
>
n
>
7
for which there exists a polynomial
p
(
x
)
p(x)
p
(
x
)
with integer coefficients such that
p
(
7
)
=
77
,
p
(
m
)
=
0
p(7) = 77, p(m) = 0
p
(
7
)
=
77
,
p
(
m
)
=
0
, and
p
(
n
)
=
85
p(n) = 85
p
(
n
)
=
85
.
polynomial
Integer Polynomial