MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
45
45
Part of
PEN A Problems
Problems
(1)
A 45
Source:
5/25/2007
Let
b
,
m
,
n
∈
N
b,m,n\in\mathbb{N}
b
,
m
,
n
∈
N
with
b
>
1
b>1
b
>
1
and
m
≠
n
m\not=n
m
=
n
. Suppose that
b
m
−
1
b^{m}-1
b
m
−
1
and
b
n
−
1
b^{n}-1
b
n
−
1
have the same set of prime divisors. Show that
b
+
1
b+1
b
+
1
must be a power of
2
2
2
.
induction
Divisibility Theory