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6
4+p_1p_2, 4+p_1p_3 are perfect squares
4+p_1p_2, 4+p_1p_3 are perfect squares
Source: BStat-BMath 2017: Problem 6
May 14, 2017
number theory
Problem Statement
Let
p
1
,
p
2
,
p
3
p_1,p_2,p_3
p
1
,
p
2
,
p
3
be primes with
p
2
≠
p
3
p_2\neq p_3
p
2
=
p
3
such that
4
+
p
1
p
2
4+p_1p_2
4
+
p
1
p
2
and
4
+
p
1
p
3
4+p_1p_3
4
+
p
1
p
3
are perfect squares. Find all possible values of
p
1
,
p
2
,
p
3
p_1,p_2,p_3
p
1
,
p
2
,
p
3
.
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