The linear congruence equation ax = b (mod n) may be rewritten as ax1 = b - nx2 where x1, x2 -E- Z. For example 25x = 15 (mod 29) may be rewritten as 25x1 = 15 - 29x2. It is possible to solve …

$\begingroup$ @Gandhi, the first two parts are standard results about linear congruences, discussed in many intro Number Theory textbooks.

Rather, this is linear algebra. Instead, you are working with a $2\times2$ linear system over a given modulus, $9$. Here, the first two elementary methods of solving linear systems apply: …

Jul 24, 2012 · When I am faced with a simple linear congruence such as $$9x \equiv 7 \pmod{13}$$ and I am working without any calculating aid handy, I tend to do something like …

Dividing the linear congruence equations. Ask Question Asked 11 years, 7 months ago.

Mar 4, 2013 · I'm trying to solve a linear congruence and I don't understand how some of them are reduced. For example, How does $105k \equiv -32 \pmod{11}\,$ reduce to $6k \equiv 1 …

Solving non-linear congruence. Ask Question Asked 12 years, 1 month ago. Modified 12 years, 1 month ago.

Solve the following linear congruences: (i) $23x \equiv 16$ mod $107$ (ii) $234x \equiv 20$ mod $366$ (iii) $234x \equiv 6$ mod $366$. I am trying to solve these through the use of the …

Jan 12, 2019 · Solving a Linear Congruence. Related. 1. Congruence Relation with exponents and variables. 1.

Mar 12, 2015 · You need to "get rid of" the $2$ from the right hand side of the first congruence in your system: \begin{aligned} 2x & \equiv 3 \mod 7 & (1) \\ x & \equiv 8 \mod 15 & (2) …