# How do I solve a modular equation (find all soloutions)?

$2(b+d) + 1(a+c) = 0 (mod 3)$

How do I go about finding all soloutions? I know this is largely related to number theory but where can I learn it? Here are a few instant ones )b=1, d=1, a=1, c=1, a=0), and (a=0, b=0, c=0,d=0), but how can I efficiently find all of them?

Also what do I do if

$2(b+d) + 1(a+c) + 2 = 0 ( mod 3)$

?

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This is a high level question, and deserves offering a bounty!

If the only values a,b,c,d can take are 0 or 1, there are at most 16 possible arrangements for theirv values. You could list them all and see in which cases the equation is satisfied.