Is it true that 1.if p is prime then n^(p squared)=n mod p for all natural numbers n?? 2. n^7=n mod 35 for all natural numbers n If so then what working should i show?and if not then what would be a counter-example??thanksss~~~
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Originally Posted by bryan06 2. n^7=n mod 35 for all natural numbers n n = 2 is a counterexample. -Dan
Originally Posted by bryan06 1.if p is prime then n^(p squared)=n mod p for all natural numbers n?? This one is true by a version of Fermat's Little Theorem. We can state that since p^2 - 1 is divisible by p - 1. So by Fermat's Little -Dan
thankss~~still a bit confused though i researched on wikipedia what fermat little theorem is but still cant figure out how you derived the following: Originally Posted by topsquark also how do you get from this line Originally Posted by topsquark since p^2 - 1 is divisible by p - 1. to this line Originally Posted by topsquark So by Fermat's Little thankss
Originally Posted by topsquark This one is true by a version of Fermat's Little Theorem. We can state that since p^2 - 1 is divisible by p - 1. So by Fermat's Little -Dan Or just note that
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