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Topic: Solving a set of simultaneous equations using modulo arithmetic
Replies: 1   Last Post: Dec 5, 1996 12:53 PM

 T.P Harte Posts: 85 Registered: 12/7/04
Re: Solving a set of simultaneous equations using modulo arithmetic
Posted: Dec 5, 1996 12:53 PM

ysr@grove.ufl.edu wrote:

: Hi,
: Could any of you please suggest a method for solving linear
: equations involving modulo arithmetic. We are not able to solve these
: using conventional methods because they involve division.

If you mean you require solutions to equations such as:

ax + by = c

then this is (re-written in modulo terms) :

ax == c (mod y), where "==" stands for a congruence

Thus, to find x, simply multiply by te inverse of a:

a^{-1}.a.x == a^{-1}c (mod y)

x == a^{-1}c (mod y)

No division is involved as a^{-1} can be calculated, provide (a,y)=1, and then
simply multiplied. But this is so simple that I'm sure that you're probably