What are the steps to solve modular linear equations?

Solving linear modular equations Main goal: categorize the methodology for solving equations ax ≡ b (mod n). Primary method for approaching these problems. Note the ax ≡ b (mod n) iff there is y ∈ Z such that ax+ ny = b (by equivalent formulation of equivalence mod n, ax ≡ b ( (mod n) iff they differ by a multiple of n). read more

In an equation \(ax \equiv b \; ( \text{mod} \; m) \) the first step is to reduce \( a \) and \( b \) mod \( m \). For example, if we start off with \( a = 28 \), \( b = 14\) and \( m = 6 \) the reduced equation would have \( a = 4\) and \( b = 2\). read more