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Thailand National Olympiad
2012 Thailand Mathematical Olympiad
2
2
Part of
2012 Thailand Mathematical Olympiad
Problems
(1)
(x -a_1)(x - a_2)...(x - a_{2012}) = (1006!)^2 has at most one integral solution
Source: Thailand Mathematical Olympiad 2012 p2
8/17/2020
Let
a
1
,
a
2
,
.
.
.
,
a
2012
a_1, a_2, ..., a_{2012}
a
1
,
a
2
,
...
,
a
2012
be pairwise distinct integers. Show that the equation
(
x
−
a
1
)
(
x
−
a
2
)
.
.
.
(
x
−
a
2012
)
=
(
1006
!
)
2
(x -a_1)(x - a_2)...(x - a_{2012}) = (1006!)^2
(
x
−
a
1
)
(
x
−
a
2
)
...
(
x
−
a
2012
)
=
(
1006
!
)
2
has at most one integral solution.
algebra
number theory
Integers