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**Questions 1. About Fermat's Little Theorem.**

**M**which I'm told implies that...

^{P-1}≡ 1 (mod P)**M**

^{P}≡ M (mod P)Is this essentially multiplying by M on both sides?? So if

**X ≡ Y ( mod P)**then

**aX ≡ aY (mod P)**?

Does.

**a⋅[ X (mod P)] = aX (mod P)**is it

**a⋅[ X (mod P)] = the remainder of X/P times a**?

Also in the Diffie Hellman exchange I'm told that...

**(g**

^{a}mod p)^{b}(mod p) = g^{ab}(mod p)which i think means in general that...

**[ g (mod p)]**)

^{a}(mod p)= g^{a}( mod pbut I'm not sure what property that uses. Can that be derived from the multiplication property where...

**ab ( mod p ) = [ a (mod p) ⋅ b (mod p) ] (mod p)**

Thanks a lot for any explanation you can give to point me on the right track.