Modulus

m mod n is the remainder of m ÷ n

1. 3 mod 5 = 3 because 3 divided by 5 is 0 with remainder 3. m mod n = n where m < n
2. 5 mod 3 = 2 because 5 divided by 3 is 1 with remainder 2. 0 <= m mod n <= n where m > n

From 1.

• 0 mod 3 = 0
• 1 mod 3 = 1
• 2 mod 3 = 2

From 2.

• 3 mod 3 = 0
• 4 mod 3 = 1
• 5 mod 3 = 2
• 6 mod 3 = 0

3. -5 mod 3 = 1 because -5 divided by 3 is -2 with remainder 1. Remainders are never negative -5 = 3(-2) + 1