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2016 Greece National Olympiad
Problems
(1)
Diophantine equation
Source: Greek National mathematical olympiad,Problem 1
2/29/2016
Find all triplets of nonnegative integers
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
and
x
≤
y
x\leq y
x
≤
y
such that
x
2
+
y
2
=
3
⋅
201
6
z
+
77
x^2+y^2=3 \cdot 2016^z+77
x
2
+
y
2
=
3
⋅
201
6
z
+
77
number theory
Diophantine equation