Hello,

I try to find somebody who will be able to answer me about the following: I hope it is not too much trouble.

May be this property can be used for searching Fermat numbers divisors.

I know this forum is not for Fermat numbers, but may be, somebody is able to answer.

If you know a forum like this one where you think somebody is able to answer, please, let me know.

I demonstrate the following property (All numbers are natural numbers)

For a composite Fermat number , I suppose it is semi-prim (even if it is not semi-prim).

For example of semi-prim, I use a little number N, let it be equal to 105.

Here, N is not semi-prim because it has 3 divisors.

I choose to considerate N like a semi-prim event if it is not.

Let

and

be

and

or

and

or

and

About Fermat numbers :

Let define the 2 divisors of

by

and

,

and

and

by:

and

So, we have the following properties (for

:

and in an equivalent way :

I try to find on the Internet some information about this property but I find nothing.

Do you know some internet sites or books about this property ?

Do you think this property can be used for searching Fermat numbers divisors?

If I'm not clear, please, let me know.

Many thanks by advance,

Best Regards,

Cyril Delestre