Compute the gcd of 135 and 170. Show all the steps of the algorithm, as in the video.

Compute the gcd of 183 and 105. Show all the steps of the algorithm, as in the video.

Consider the equation $7x + 15y = 1$. Find an integer solution to this equation using inspection or trial and error.

Using the previous problem, tell me the inverse of $7$ modulo $15 and the inverse of $15$ modulo $7$. (This should require no computation, just look at the previous problem and have an aha moment!)