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2006 Swedish Mathematical Competition
6
Equation with Exponents
Equation with Exponents
Source: 2006 Swedish Mathematical Competition #6
January 5, 2018
algebra
Exponents
Sweden
Problem Statement
Determine all positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfying
a
(
b
c
)
=
(
b
a
)
c
a^{(b^c)}=(b^a)^c
a
(
b
c
)
=
(
b
a
)
c
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