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Contests
National and Regional Contests
PEN Problems
PEN H Problems
75
75
Part of
PEN H Problems
Problems
(1)
H 75
Source:
5/25/2007
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
.
Diophantine Equations
pen