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Junior Balkan MO
2015 Junior Balkan MO
1
Jbmo 2015 problem 1
Jbmo 2015 problem 1
Source:
June 26, 2015
number theory
prime numbers
Problem Statement
Find all prime numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
and positive integers
k
k
k
satisfying the equation
a
2
+
b
2
+
16
c
2
=
9
k
2
+
1.
a^2+b^2+16c^2 = 9k^2 + 1.
a
2
+
b
2
+
16
c
2
=
9
k
2
+
1.
Proposed by Moldova
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