MathDB
Problems
Contests
National and Regional Contests
Italy Contests
ITAMO
2023 ITAMO
1
1
Part of
2023 ITAMO
Problems
(1)
Easy equation with powers
Source: Italy MO 2023 P1
5/7/2023
Let
a
,
b
a, b
a
,
b
be positive integers such that
5
4
a
=
a
b
54^a=a^b
5
4
a
=
a
b
. Prove that
a
a
a
is a power of
54
54
54
.
number theory