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11
Solve the equation
Solve the equation
Source:
September 8, 2010
number theory
equation
polynomial
Diophantine equation
IMO Shortlist
Problem Statement
Let
n
n
n
be a positive integer and
a
1
,
a
2
,
…
,
a
2
n
a_1, a_2, \dots , a_{2n}
a
1
,
a
2
,
…
,
a
2
n
mutually distinct integers. Find all integers
x
x
x
satisfying
(
x
−
a
1
)
⋅
(
x
−
a
2
)
⋯
(
x
−
a
2
n
)
=
(
−
1
)
n
(
n
!
)
2
.
(x - a_1) \cdot (x - a_2) \cdots (x - a_{2n}) = (-1)^n(n!)^2.
(
x
−
a
1
)
⋅
(
x
−
a
2
)
⋯
(
x
−
a
2
n
)
=
(
−
1
)
n
(
n
!
)
2
.
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