Modular arithmetic
Number theory
Arithmetic in which numbers wrap around on reaching a fixed modulus n, so that a and b are treated as equal when n divides a − b.
What is usually left out
This is the standard tool for proving something is impossible. Showing an equation has no solutions modulo some small n rules out integer solutions entirely, and often in a line. The converse does not hold: solvability modulo every n does not guarantee an integer solution, and the gap between the two is the subject of the local-global principle.