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24
2007 Guts #24: How Many Ordered Triples
2007 Guts #24: How Many Ordered Triples
Source:
June 22, 2012
Problem Statement
Let
x
,
y
,
n
x,y,n
x
,
y
,
n
be positive integers with
n
>
1
n>1
n
>
1
. How many ordered triples
(
x
,
y
,
n
)
(x, y, n)
(
x
,
y
,
n
)
of solutions are there to the equation
x
n
ā
y
n
=
2
100
x^n-y^n=2^{100}
x
n
ā
y
n
=
2
100
?
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