Calculating , modulo:

Question

I need help to understand this.

Y = 17i+7 mod26

If Y value was known, can we calculate i value? If YES, how? If NO, why?

And if i write it like this, is it the same or not, and why? :

Y = (17i+7) mod26 

Thank you

Answer 1

Let's look at your second answer first: Adding parenthesis should not change anything, so I'd say it's the same. However, some people might give different meanings to these notations, so in the end it depends on the notations you use and learned, try to look them up.

Now for the question how to compute $i$ from $Y$: We can compute $17i \equiv Y-7 \mod 26$ and hence need to find a number $a$ such that $17a \equiv 1 \mod 26$. If we had such an $a$, we would get $i \equiv a(Y-7) \mod 26$ and we're done. Now such an $a$ exists in this case, and it can be computed using the extended Euclidian algorithm - are you familiar with how this works?