This has to do with how cryptography or at least some form of it is implemented.
I'm asked to solve an equation in the form j . k . j= 1 (mod z) z being a "totient" (the result of two primes p and q where z=(p-1)(q-1)) and k a prime number such as z non divisible by k
My prime numbers are p=2, q=3
z= 2
k=5
Back to the equation:j . k . j= 1 (mod z)
I'm told its int the form xy= 1 (mod n)...first I don't see why the original form is like what I'm told, but lets pass on this..(maybe someone can help me understand why later on) According to a rule, we can write 5x+2y =1 in the form of a= c(mod b) so: 5x= 1 (mod 2)
I choose to use mod 5 to isolate x (I'm not sure if I can do that but using the inverse doesn't help)
5(5x)= 5 (mod 2)
x= 5 (mod 2)
x= 5 + 2k
By replacing in 5x+2y =1
5(5 +2k) + 2y =1
25 + 10k +2y =1
2y = -25 -10k +1
2y = -24 -10k
y = -12 -5k
My question...Am I right and if not how to proceed? Thank you in advance for your help.