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hartnn
 3 years 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
hartnn
 3 years 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

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hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3@siddhantsharan , @sauravshakya

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3yes, that was direct use of the theorem....

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0i think we just use it directly

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3any other interesting topic or theorem in modular arithmetic ?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0Wilson's theorem is interesting

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

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

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

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1FLT is also a^p = a (mod p) Show that the two formulations are equivalent.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3divide by a on both sides? maybe.....

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1It's an iff type, so both ways......

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

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1On the right track, sort of...

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1a^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...

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3same for other part, right ?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1Yes, more or less.....

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1FLT is also used in some combinatorial problems....

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3u have some practice/examples with those ?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1OK, 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?

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

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1Or I can tell you the answer and you can try to work it out.....

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3let me try....after few minutes, u give answer...

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1I think u need more than a few minutes....:)

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1(n^pn)/2p + (n^((p+1)/2) n)/2 + n

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1It's an integer so the first term still incorporates FLT...

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1Do you want links only about FLT/Wilsons or congruences/modular stuff as well....

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.3modular stuff as well...

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

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