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Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
11
11
Part of
PEN H Problems
Problems
(1)
H 11
Source:
5/25/2007
Find all
(
x
,
y
,
n
)
∈
N
3
(x,y,n) \in {\mathbb{N}}^3
(
x
,
y
,
n
)
∈
N
3
such that
gcd
(
x
,
n
+
1
)
=
1
\gcd(x, n+1)=1
g
cd
(
x
,
n
+
1
)
=
1
and
x
n
+
1
=
y
n
+
1
x^{n}+1=y^{n+1}
x
n
+
1
=
y
n
+
1
.
Diophantine Equations