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# Use Fermat's theorems to prove the following formulas?

Fermat's Theorem If p is a prime, a is a natural number, then p / (a^p - p)

I) p / (1+2+3+...+(p-1)

II) p / (1^p+2^p+3^p...+(p-1)^p)

III) p/ (1^(p-1)+2^(p-1)+3^(p-1)...+(p-1)^(p-1) +1)

Can someone help me out?

### 2 Answers

- Anonymous8 years agoFavorite Answer
Your statement is incomplete. Study the theorem here: https://en.wikipedia.org/wiki/Fermat%27s_little_th...

Fermat's other theorems are here: https://en.wikipedia.org/wiki/Fermat%27s_theorem

- moranoLv 44 years ago
All of that is senseless in any respect, your 4th. variety question risk-free. Sorry to be so direct P.S. The sentence "x is the consumer-friendly term between a,b and c" isn't an often defined terminology, in case you want to apply it you ought to define that, is it x=GCD(a,b,c) the proper consumer-friendly Divisor? etc... make an effort to work out what a theorem or any mathematical assertion extremely potential. once you assert, as an occasion: "all of us understand , a^(n)=c^(2)-b^(2)" you ought to define which a,b,c are, are they any 3 integers? or you advise "enable a,b,c are 3 integers verifing that equation"; or you're making in common terms confusion for your self and for others, that's no longer sensible to you, actual that's no longer arithmetic. in case you extremely love arithmetic (as i will music out of your interest) take time to earnings the widely used mathematical language first, and the coolest judgment in the back of each and each math techniques. i think of you're able to do good issues with slightly bit greater of humility and of path which incorporate your interest related to information and readability. thank you on your interest