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## Main Question or Discussion Point

I'm trying to better understand RSA and Diffie-Hellman exchange and the modulus math that they are base on, there are some questions I have about there properties for which I am unable to find concise explanations about. I'm generally interested in how the commutative, associative, distributive, etc.. properties apply.

Is this essentially multiplying by M on both sides?? So if

Does.

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

which i think means in general that...

but i'm not sure what property that uses. Can that be derived from the multiplication property where...

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

**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.