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2017 Greece Junior Math Olympiad
3
3
Part of
2017 Greece Junior Math Olympiad
Problems
(1)
1\p=1/a^2+1/b^2 diophantine with prime p (Greece Juniors 2017 p3)
Source:
3/16/2020
Find all triplets
(
a
,
b
,
p
)
(a,b,p)
(
a
,
b
,
p
)
where
a
,
b
a,b
a
,
b
are positive integers and
p
p
p
is a prime number satisfying:
1
p
=
1
a
2
+
1
b
2
\frac{1}{p}=\frac{1}{a^2}+\frac{1}{b^2}
p
1
=
a
2
1
+
b
2
1
Diophantine equation
diophantine
number theory