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PEN A Problems
33
A 33
A 33
Source:
May 25, 2007
Divisibility Theory
Problem Statement
Let
a
,
b
,
x
∈
N
a,b,x\in \mathbb{N}
a
,
b
,
x
∈
N
with
b
>
1
b>1
b
>
1
and such that
b
n
−
1
b^{n}-1
b
n
−
1
divides
a
a
a
. Show that in base
b
b
b
, the number
a
a
a
has at least
n
n
n
non-zero digits.
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