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# How do you use mods? The algebraic kind, I mean.?

The title says it all, really, but I'm not sure if that's how 'mods' is spelled; it just sounded like that.

Basically, you can use them to solve problems like this:

2y+5x= 125

or at least it will give you one of the answers. Like you use "mod 5" or something.

### 1 Answer

- MathMan TGLv 71 decade agoFavorite Answer
Mod is short for "modulus" and you solve Diophantine equations such as this

(where there are more variables than equations and you desire integer solutions)

using them.

In this case it's fairly simple:

125 divides by 5 (it is congruent to 0 mod 5, as they say),

so there is an immediate solution of

y = 0, x = 25

Then you can find other solutions by varying x by 2 in one direction

(adding or subtracting 10 to the total)

and varying y by 5 in the other direction

(reversing the change by 10 from x).

So you have y = 5 and x = 23

or y = -5 and x = 27

and so on

y = 0 + 5t

x = 5 - 2t

for all integers t.