MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
78
78
Part of
PEN H Problems
Problems
(1)
H 78
Source:
5/25/2007
Let
x
,
y
x, y
x
,
y
, and
z
z
z
be integers with
z
>
1
z>1
z
>
1
. Show that
(
x
+
1
)
2
+
(
x
+
2
)
2
+
⋯
+
(
x
+
99
)
2
≠
y
z
.
(x+1)^{2}+(x+2)^{2}+\cdots+(x+99)^{2}\neq y^{z}.
(
x
+
1
)
2
+
(
x
+
2
)
2
+
⋯
+
(
x
+
99
)
2
=
y
z
.
Diophantine Equations
pen