+266 "Modulo graph paper" consists of a grid of \(m^2\) 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 \(y\equiv x^2\pmod 5\) would consist of the points \((0,0),(1,1),(2,4),(3,4),(4,1)\) .
The graphs of
\(y\equiv 5x+2\pmod{16}\)
and
\(y\equiv 11x+12\pmod{16}\)
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.
+288 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?
+266 hm... what do you mean by edit my answer further. I don't quite understand
