a Suppose you know that 757 11 mod 101 and that 29 7 mod 101

a) Suppose you know that 7^57 11 (mod 101) and that 2^9 7 (mod 101). Find y such that 7^y 2 (mod 101)

Here a=bmod c means that (a-b) is divided by c.

That means 7^57 =11 mod (101) i.e. (7^57 -11 ) is divided by 101 or in 2^9=7mod(101) i.e. (2^9-7) =512-7 =505

that is surely divided by 101 or (2^9-7) = 101 x 5

Again 7^y=2mod(101) i.e. (7^y-2) is divided by 101, then it is only possible when y=39 as

7^(39)-2 is always completely divisible by 101

So correct answer is y= 39