Section 2.2
Linear congruences
In addition to the first-degree equation ax = b
with integer coefficients,
we can also study the related equation ax = b mod n, a
linear congruence.
Let a, b 
Z.
Theorem
Let n be a positive integer. Consider the equation ax = b mod n.
Let n be a positive integer. Consider the equation ax = b mod n.
- The equation is solvable if and only if gcd(a,n) | b.
- If gcd(a,n) | b, then there are gcd(a,n) solutions modulo n.
Of course, solving a linear congruence ax = b mod n
is closely related to solving the diophantine equation ax + ny = b discussed in Section 1.3.