How many ordered pairs of integers (a, b) are needed to guarantee that there are two ordered pairs (a1, b1) and (a2, b2) such that a1 mod 5

I’m a smart person so that’s why i think it was 6

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.