Many problems about divisibility can be solved using algebraic identities such as:
- {}
for all
and
for all odd
.
- Note that
provided that
.
- (Sophie Germain’s identity)
Here is a problem which can be solved using algebraic identities:
Example:
Show that is not a prime for
.
Solution:
Note that
which in turn equals
, that is,
Since , each
,
is greater than 1. Hence,
is not prime for
.
More later,
Nalin Pithwa