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JBMO Shortlist 2020 N2
JBMO Shortlist 2020 N2
Source: JBMO Shortlist 2020
July 4, 2021
Junior
Balkan
shortlist
2020
number theory
prime numbers
Problem Statement
Find all positive integers
a
a
a
,
b
b
b
,
c
c
c
, and
p
p
p
, where
p
p
p
is a prime number, such that
73
p
2
+
6
=
9
a
2
+
17
b
2
+
17
c
2
73p^2 + 6 = 9a^2 + 17b^2 + 17c^2
73
p
2
+
6
=
9
a
2
+
17
b
2
+
17
c
2
.
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