Question

The inverse of /a/ modulo 39 is /b/. What is the inverse of /4a/ modulo 39 in terms of /b/?

Give your answer as an expression in terms of /b/.

Answer 1

\(ab = 1 \mod 39 \) is what you say
\(4ac = 1 \mod 39\) for some \(c\).

I suggest you write \(c\) as \(bd\) and find \(d\).

Answer 2

Write : \((4a)(bd) = 1\) and use associativity
https://proofwiki.org/wiki/Modulo_Multiplication_is_Associative

Answer 3

That would become \(4(ab)d = 1 \mod 39\). And what happens to this \((ab)\) ? do you see?

Answer 4

ab = 1 in mod 39 so it cancels out right @reemii

Answer 5

Yes, you now have to find \(d\) based on what's left in hte equation, ...

Answer 6

So 4d == 1 (mod 39)...

4d == 40 (mod 39)

d == 10 (mod 39)

@reemii

Answer 7

I think so too. :-)

Answer 8

let me check..

Answer 9

test...
a=8, b=5.
4a = 32, 10b = 50 => 4a * 10b = 1600. That is 41*39 + 1.. phew.

Answer 10

Well, it's correct. (the argumentation is correct) The example is just to illustrate.

Answer 11

so the answer would be 10b, correct?

@reemii

Answer 12

yes

Answer 13

thanks so much for your help! @reemii

Answer 14

glad I could help ;-)