MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
75
H 75
H 75
Source:
May 25, 2007
Diophantine Equations
pen
Problem Statement
Let
a
,
b
a,b
a
,
b
, and
x
x
x
be positive integers such that
x
a
+
b
=
a
b
b
x^{a+b}=a^b{b}
x
a
+
b
=
a
b
b
. Prove that
a
=
x
a=x
a
=
x
and
b
=
x
x
b=x^{x}
b
=
x
x
.
Back to Problems
View on AoPS