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December 8th, 2015, 08:18 AM   #1
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what's up with FlT?

So much was written and discussed here about Fermats Last theorem.
But no one talks about Fermats little theorem!

What do we know about pseudoprimes?
What do we know about their distribution and characteristics?

Say if we test for Fermat pseudoprimes to base 2 we get:
A001567 [341, 561, 645, 1105, 1387, 1729, 1905 ...]

for testing base 2 and 3:
A052155 [1105, 1729, 2465, 2701, 2821, 6601, 8911 ...]

for base 2 and 3 and 5:
A083737 [1729, 2821, 6601, 8911, 15841, 29341, 41041 ...]

And so on ...

A lot of those pseudoprimes are Carmichael numbers, but few are not.


Please let me know:
If we and-test for all Fermat pseudoprimes to bases [2,3,5,7,11,...,97] (the first 25 primes)
what is the smallest pseudoprime to those bases, that is not a Carmichael number?

Would be nice to post the correct answer before X-mas
Thanks in advance!

Last edited by Martin Hopf; December 8th, 2015 at 08:29 AM.
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December 9th, 2015, 05:34 AM   #2
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What is your point? "Fermat's last theorem" gets a lot of discussion because it was unproved for a very long time, the valid proof requiring quite deep mathematics.

"Fermat's little theorem", on the other hand, was proved by Euler in 1736, almost 300 years ago!
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December 9th, 2015, 06:22 AM   #3
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Quote:
Originally Posted by Country Boy View Post
What is your point? "Fermat's last theorem" gets a lot of discussion because it was unproved for a very long time, the valid proof requiring quite deep mathematics.
The Last Theorem gets a lot of discussion from cranks who think that just because it took a professional mathematician and research professor 200 pages of "quite deep mathematics" to prove a theorem that countless of the best mathematical minds throughout history failed so to do, shouldn't stop them from proving it on the back of an envelope using bad high-school mathematics.

Last edited by v8archie; December 9th, 2015 at 06:24 AM.
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December 21st, 2015, 09:31 AM   #4
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Quote:
Originally Posted by Martin Hopf View Post
If we and-test for all Fermat pseudoprimes to bases [2,3,5,7,11,...,97] (the first 25 primes)
what is the smallest pseudoprime to those bases, that is not a Carmichael number?
Hint: the last digit of this number should be 1.
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