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2011 LMT
18
18
Part of
2011 LMT
Problems
(1)
2011 Spring LMT Individual Round Problem 18
Source:
9/11/2023
Let
x
x
x
and
y
y
y
be distinct positive integers below
15
15
15
. For any two distinct numbers
a
,
b
a, b
a
,
b
from the set
{
2
,
x
,
y
}
\{2, x,y\}
{
2
,
x
,
y
}
,
a
b
+
1
ab + 1
ab
+
1
is always a positive square. Find all possible values of the square
x
y
+
1
xy + 1
x
y
+
1
.
number theory