To solve following system of equivalences of integers

Question

To solve following system of equivalences of integers

$x \equiv 2 \pmod {15}$

$x \equiv 4 \pmod {21}$

The number of solutions in x, where $1\leq x\leq 315$ is

A. 0

B. 1

C. 2

D. 3

So i have to find number of numbers such that when 2 and 4 are subtracted from them they get divided by 15 and 21. But how do i do it?

Thanks

Answer 1

we have $x=2+15k_1$ and $x=4+21k_2$ from here we get $$15k_1-21k_2=2$$ with $k_1,k_2$ integer numbers. what can we say about the solutions of this equation?