Question

the inverse of a modulo 39 is b. what is the inverse of 4a modulo 39 in terms of b.

Answer 1

Okay. Sure.

Answer 2

@douglaswinslowcooper or @SithsAndGiggles ... u guys would be pretty good at these, lil help...?

Answer 3

you are familiar with ring theory?

Answer 4

No.

Answer 5

or group theory?

Answer 6

No, the lesson was on residues and modular inverses. We haven't learned those theories yet.

Answer 7

okay it might be wrong. but I'll just write it down. have my exam tomorrow so won't be able to discuss it :] So, inverse of a is b. You could write ab=39q+1. So, 4ab=39q'+4. Which implies 40ab=39q''+40=39q''+39+1=39(q''+1)+1 which can be rewritten as (4a)(10b)=39Q+1 which means (10b)(4a)=(mod39) . So, 10b is the modular inverse of 4a. (If that's what you meant by inverse here)

Answer 8

Its a wile since i did this stuff but if i remember correctly
if we let a be the inverse Mod 39 of b then

a * b = 1 (mod 39)

Answer 9

yeah I used this definition.

Answer 10

yes looks like nipunmalnotra93's solution is correct

Answer 11

Only ring theory I knew was about engagements and weddings.

Answer 12

Lol. Speaking of which, this could be verified using ring theory. A homomorphism from f: Z->Z(39) where f(a)=a(mod39) can be used to verify f((4a)(10b))=f((40)(ab))=f(40)f(ab)=1.1=1.

Answer 13

yeah the answer is 10b.

Thanks!