1. ## Modulo problem

Hi!

I am very new at this modulo arithmetic, and don´t know who to interpret this problem.

Let N = 2*3*5*7*........*101 + 1

Find the smallest positive integer for which $N \equiv x\ (\bmod y)$
if y = 2.

Thanks!

2. $N \equiv 1 \: \left(\text{mod} \: 2\right)$

Why? Because N is an odd number (you have an even number + 1) and any odd number leaves a remainder of 1 (this is x) when divided by 2 (your modulus).

3. ## hi

Hi!

Yes of course, there is a 2 at the beginning! So N has to be odd because we add one at the end.

Thanks!