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1995 AIME Problems
8
Fractions Equal Integers
Fractions Equal Integers
Source:
December 22, 2005
AMC
AIME
Problem Statement
For how many ordered pairs of positive integers
(
x
,
y
)
,
(x,y),
(
x
,
y
)
,
with
y
<
x
≤
100
,
y<x\le 100,
y
<
x
≤
100
,
are both
x
y
\frac xy
y
x
and
x
+
1
y
+
1
\frac{x+1}{y+1}
y
+
1
x
+
1
integers?
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