+307 "Modulo graph paper" consists of a grid of m2 points, representing all pairs of integer residues (x,y) where\(0\le x . 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≡x2(mod5) would consist of the points (0,0),(1,1),(2,4),(3,4),(4,1) .
The graphs of
y≡5x+2(mod16)
and
y≡11x+12(mod16)
on modulo 16 graph paper have some points in common. What is the sum of the -coordinates of those points?
By the Euclidean Algorithm, the y-intercept is (7,18), so the answer is 7 + 18 = 25.
+289 5x + 2 = 11x + 12 (mod 16)
6x = -10 (mod 16)
6x = 6 (mod 16)
3x = 3 (mod 8)
Inverse of 3 in mod 8 is 3.
x = 1 (mod 8)
believe that the range for x are [0, m) based on my inferences. If I am wrong, let me know.
Then, all x values that satisfy this equation in those boundaries are 1 and 9.
Hence, the coordinates of the points are (1, 7), (9, 15).
Now, can you solve the question from here?
+307 hm... what do you mean by edit my answer further. I don't quite understand
