MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
Taiwan National Olympiad
1999 Taiwan National Olympiad
1
1
Part of
1999 Taiwan National Olympiad
Problems
(1)
integer equation
Source: 8-th Taiwanese Mathematical Olympiad 1999
1/20/2007
Find all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of positive integers such that
(
x
+
1
)
y
+
1
+
1
=
(
x
+
2
)
z
+
1
(x+1)^{y+1}+1=(x+2)^{z+1}
(
x
+
1
)
y
+
1
+
1
=
(
x
+
2
)
z
+
1
.
number theory proposed
number theory