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2016 Ecuador Juniors
2
2
Part of
2016 Ecuador Juniors
Problems
(1)
(x + 1)^2 + (x + 2)^2 +...+ (x + 9)^2 = y^2 2016 Ecuador NMO (OMEC) 3.1 2.2
Source:
9/17/2021
Prove that there are no positive integers
x
,
y
x, y
x
,
y
such that:
(
x
+
1
)
2
+
(
x
+
2
)
2
+
.
.
.
+
(
x
+
9
)
2
=
y
2
(x + 1)^2 + (x + 2)^2 +...+ (x + 9)^2 = y^2
(
x
+
1
)
2
+
(
x
+
2
)
2
+
...
+
(
x
+
9
)
2
=
y
2
diophantine
Diophantine equation