Let k be a positive integer such that are all prime numbers, and put

Show that

Deduce that if then .

Conclude that if that is, that m is a Carmichael number.

I am stumped...

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- Dec 15th 2009, 02:34 PMcomssaproof with carmichael numbers
Let k be a positive integer such that are all prime numbers, and put

Show that

Deduce that if then .

Conclude that if that is, that m is a Carmichael number.

I am stumped... - Dec 15th 2009, 06:06 PMiknowwhatyoudidlastsummer
Maybe you should have gone to Norin's office hours?

- Dec 15th 2009, 06:31 PMBruno J.
(Rofl)

That's pretty funny. Now stop stalking each other, guys. - Dec 15th 2009, 08:28 PMchiph588@

It's easy to see that , , .

by Fermat's Little Theorem.

From above we now know .

Therefore .

since we have an integer cubed.

Therefore .

i.e. .