Hello, i dont know if you have the time but i've a question about Euler theorem. Let say you want to find phi(26), how do you do that ? without calculator. I dont understand how most teacher calculate phi so fast. (2-1)(13-1) = 12 We says that 2 divide 13 integers between 1 and 26, where does 13 come from ? I understand fermat little theorem but euler theorem..
I've find the answer somewhere, you have to divide 26 by 2 and once the rest is equal to 0 we divide the quotient by 2 redo til the rest is equal to 1. 26 = 2x13 + 0
The letter 'n', underlined and written as a superscript. It's a way of shortening words on paper. Can't reproduce here, but Solution becomes Soln, Definition can be written Defn, Abbreviation as Abbrevn.
The solution is 4 (mod 8), so anything of the form 4 + 8k will work. We originally wanted to solve in mod 32, so any value of k is fine as long as it yields a number between 0 and 31, so that's the final list of solutions: 4, 12, 20, 28.
Because our original goal was to solve a congruence modulo 32. I guess this isn't strictly necessary, but it is customary to exhibit your solution in terms of the original congruence.
@@MichaelPennMath thanks for replying me very fastly sir.I am from India and after going through lots of videos now i am able to understand the concept by you.may i know from which country and region you belong to?
I hated this as a student as well! It is so much more efficient to guess and check modular inverse for "small" n rather than go through the trouble of doing the Extended Euclidean Algorithm. Here is a video where I highlight the guess and check method along with the long method: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uPFh9_nLw1c.html. Also, lots of research level mathematics is done via guess and check. The checking just involving writing a careful proof.
