Math help

Yes, someone here probably knows how to solve the problem but that should not be the question you are asking. This is a math help site so you should be asking if someone could help you solve the problem.
In addition to giving us the problem you need to show us your attempt in solving this problem so we know where you seem to be having troubles. In that way we can offer you the help you need to solve your problem.

So please post the problem and show us your work.
 
The problem is to show that, for any n and p a prime, n^p= n (mod p) and you are told to "use induction". Do you know what that is? Do you know what "(mod p)" means? I have to ask those questions because you didn't show any attempt yourself so we don't know what you, yourself, understand about this problem. (And it would have been simpler for everyone if you had just typed the problem in here!)

When n= 1, what is 1^p? Now, suppose it is true that, for some n= k, k^p= k (mod p). What can you say about (k+1)^p (mod p)? As the hint says, use the binomial formula and remember that any multiple of p is 0 "mod p".
 
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