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3.
3.
Part of
2017 Polish Junior Math Olympiad Finals
Problems
(1)
2017 Polish Junior Math Olympiad Finals P3
Source: 2017 Polish Junior Math Olympiad Finals
5/22/2023
Positive integers
a
a
a
and
b
b
b
are given such that each of the numbers
a
b
ab
ab
and
(
a
+
1
)
(
b
+
1
)
(a+1)(b+1)
(
a
+
1
)
(
b
+
1
)
is a perfect square. Prove that there exists an integer
n
>
1
n>1
n
>
1
such that the number
(
a
+
n
)
(
b
+
n
)
(a+n)(b+n)
(
a
+
n
)
(
b
+
n
)
is a perfect square.
number theory