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

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