MathDB

The

{<span class='latex-italic'>distinct prime factors</span>}

of an integer are its prime factors listed without repetition. For example, the distinct prime factors of

40

are

2

and

5

.
Let

A=2^k - 2

and

B= 2^k \cdot A

, where

k

is an integer (

k \ge 2

). Show that, for every integer

k

greater than or equal to

2

,
[*]

A

and

B

have the same set of distinct prime factors. [*]

A+1

and

B+1

have the same set of distinct prime factors.

3