"Modulo m graph paper" consists of a grid of m^2 points, representing all pairs of integer residues (x,y) where 0 < x < m. To graph a congruence on modulo m graph paper, we mark every point (x,y) that satisfies the congruence. For example, a graph of y == x^2 mod{5} would consist of the points (0,0), (1,1), (2,4), (3,4), and (4,1). The graph of 3x == 4y-1 mod{35} has a single x-intercept (x_0,0) and a single y-intercept (0,y_0), where 0 < x_0, y_0 < 35. What is the value of x_0+y_0?

Guest Aug 1, 2018