In simple terms, Modular Arithmetic calculates the remainder of anything divided by anything. The later is called modulus. e.g. ( 15 / 7 ) Quotient: 2, Remainder 1. In greater sense, modular arithmetic is a system of arithmetic for integers , where numbers "wrap around" upon reaching a certain value—the modulus ( src: Wikipedia ). Take a look at hour clock. After 12:59 pm, we say 1:00 pm, because we modulo the hours by 12. 13 pm % 12 is 1 pm. (%) represents modulus operator. Examples: 5 % 2 = 1, 14458948 % 25 = 23 a≡b (mod n) This says that a A is congruent to b modulo n. It means both a and b has same remainder when divided by n. e.g. 38 ≡14 (mod 12) Commonly Used Properties: Reflexivity: a ≡ a (mod n ) Symmetry: a ≡ b (mod n ) if and only if b ≡ a (mod n ) Transitivity: If a ≡ b (mod n ) and b ≡ c (mod n ) , then a ≡ c (mod n ) If a 1 ≡ b 1 (mod n ) and a 2 ≡ b 2 (mod n ), or if a