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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- Apr 25th 2011, 09:21 AMbryan06Mod and primes?!
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~~~ - Apr 25th 2011, 09:42 AMtopsquark
- Apr 25th 2011, 09:47 AMtopsquark
This one is true by a version of Fermat's Little Theorem. We can state that

http://latex.codecogs.com/png.latex?...t{(mod p - 1)}

since p^2 - 1 is divisible by p - 1. So by Fermat's Little

http://latex.codecogs.com/png.latex?...\text{(mod p)}

-Dan - Apr 26th 2011, 11:27 AMbryan06
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:also how do you get from this line to this line

thankss - Apr 26th 2011, 04:27 PMDrexel28
Or just note that http://latex.codecogs.com/png.latex?...n\text{ mod }p