INTRODUCTION TO CONGRUENCES

1. Congruence are useful tool in the study of _______.

A complete residue system is simply a set containing precisely ___ representative of each residue class modulo n.

If 17¹¹³ is divided by 3 we can get a remainder of ___.

Inverse of 15 ∈ Z sub 26 is equals to ___.

If a and b leave the same remainder when divided by a third number m, then we say a is ___ to b modulo m.

The theory of congruences was developed by ____________.

The ______ property states that if a ≡ b (mod m), then b ≡ a (mod m).

The ______ property states that if a ≡ b (mod m) and b ≡ c (mod m), then a ≡ c (mod m).

At the beginning of the ______ century, theory of congruences was developed.

In congruences, we let m be a ______ integer.