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Fermat's Little Theorem.
a^{p1}=(corresponds to)1mod p
using this, we have remainder when 3^100 is divided by 101 as 1.
Is this correct ?
Can i have few more examples where this theorem is applied but not so directly...
@mukushla
 one year ago
 one year ago
Fermat's Little Theorem. a^{p1}=(corresponds to)1mod p using this, we have remainder when 3^100 is divided by 101 as 1. Is this correct ? Can i have few more examples where this theorem is applied but not so directly... @mukushla
 one year ago
 one year ago

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hartnnBest ResponseYou've already chosen the best response.3
@siddhantsharan , @sauravshakya
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
yes, that was direct use of the theorem....
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
i think we just use it directly
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
any other interesting topic or theorem in modular arithmetic ?
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
Wilson's theorem is interesting
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
(n1)!=1(mod n) how do we use it ?
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
If \(p\) is a prime, then \((p1)!+1\) is a multiple of \(p\), that is\[(p1)! \equiv 1 \ \ \text{mod} \ p\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
i will be glad if someone posts a link for a good reference in this topic...
 one year ago

estudierBest ResponseYou've already chosen the best response.1
FLT is also a^p = a (mod p) Show that the two formulations are equivalent.
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
divide by a on both sides? maybe.....
 one year ago

estudierBest ResponseYou've already chosen the best response.1
It's an iff type, so both ways......
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
idk....maybe multiply both sides by a to get a^p = a (mod p) but is it correct to do so ?
 one year ago

estudierBest ResponseYou've already chosen the best response.1
On the right track, sort of...
 one year ago

estudierBest ResponseYou've already chosen the best response.1
a^p = a mod p, then if a not = 0 mod p then can cancel by a to get a^(p1) = 1 mod p That's the first part...
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
same for other part, right ?
 one year ago

estudierBest ResponseYou've already chosen the best response.1
Yes, more or less.....
 one year ago

estudierBest ResponseYou've already chosen the best response.1
FLT is also used in some combinatorial problems....
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
u have some practice/examples with those ?
 one year ago

estudierBest ResponseYou've already chosen the best response.1
OK, you can try this one: Say you have enough beads in n colours, how many different necklaces consisting of p beads can be made, where p is prime?
 one year ago

estudierBest ResponseYou've already chosen the best response.1
I guess I should tell you that you will need to think a bit in order to work it out, it is not straightforward....
 one year ago

estudierBest ResponseYou've already chosen the best response.1
Or I can tell you the answer and you can try to work it out.....
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
let me try....after few minutes, u give answer...
 one year ago

estudierBest ResponseYou've already chosen the best response.1
I think u need more than a few minutes....:)
 one year ago

estudierBest ResponseYou've already chosen the best response.1
(n^pn)/2p + (n^((p+1)/2) n)/2 + n
 one year ago

estudierBest ResponseYou've already chosen the best response.1
It's an integer so the first term still incorporates FLT...
 one year ago

estudierBest ResponseYou've already chosen the best response.1
Do you want links only about FLT/Wilsons or congruences/modular stuff as well....
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
modular stuff as well...
 one year ago

estudierBest ResponseYou've already chosen the best response.1
Similar this http://www.math.sc.edu/~filaseta/gradcourses/Math780notes.pdf Or more detailed....
 one year ago

hartnnBest ResponseYou've already chosen the best response.3
thanks, i'll go through it......and will ask u for any doubts.
 one year ago
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