How Does Fermat's Little Theorem Apply to Calculating 3^302 (mod 5)?

[1+1=1]

I have a question regarding mods and Fermat's Little Theorem. I know Fermat's little theorem states that a^p-1 congruent to 1 (mod p). Also, i know that for every interger a we have that a^p congruent to a (mod p). So, my question is: What is the answer for 3^302 (mod 5)? Would it be 3^301 congruent 1 (mod 5)? I am having a bit of difficulty understanding this concept. Any help?

 

[Hurkyl]

Well, Fermat's little theorem says 3^(5-1) = 1 (mod 5)...

 

[Zurtex]

Consider 300 = 4*75 = (5-1)*75. So:

So 3^(302) mod 5 = 3*3*[3^(300)] mod 5 = 3*3*[(3^75)^(5 - 1)] mod 5 = 3*3*1 mod 5

I think you can do the rest

 

[1+1=1]

thank you thank you all. by using this i can figure out the other five problems.