Fermat’s Theorem

**extatic** · September 27th 2011, 05:51 PM

Hi Guys,

In my information security class, been receiving a couple of these questions, i am able to do it by breaking them down and calculating them.

However my teacher told me NOT to calculate them and i can answer it just by looking at the questions.

If you guys can break any of these down with as much information as you can that would be really great.

Use Fermat’s Theorem compute:

$2^6\ mod \7$

$97^{130} \mod \131$

$51^{22} \mod \23$

**chisigma** · September 27th 2011, 06:41 PM

Originally Posted by extatic

Hi Guys,

In my information security class, been receiving a couple of these questions, i am able to do it by breaking them down and calculating them.

However my teacher told me NOT to calculate them and i can answer it just by looking at the questions.

If you guys can break any of these down with as much information as you can that would be really great.

Use Fermat’s Theorem compute:

$2^6\ mod \7$

$97^{130} \mod \131$

$51^{22} \mod \23$

Fermat's [little] theorem: if p is prime and p doesn't devide a then $a^{p-1}\equiv\ 1\ \text{mod}\ p$ ...

Your cases...

a) 7 is prime and 7 doesn't devide 2 $\implies 2^{6} \equiv\ 1\ \text{mod}\ 7$

b) 131 is prime and 131 doesn't devide 97 $\implies 97^{130} \equiv\ 1\ \text{mod}\ 131$

a) 23 is prime and 23 doesn't devide 51 $\implies 51^{22} \equiv\ 1\ \text{mod}\ 23$

Kind regards

$\chi$ $\sigma$

**extatic** · September 27th 2011, 06:52 PM

thank you soo much, awesome help.

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