Today, I want to share some divisibility cum remainder tests that I have created myself for 7, 11, 13, 17, 19. There are more to come.
Reference example:
Prime Number (p) ( a, b, c, cycle goes on. )
Take a number for example:
966 mod p = 6a + 6b + 9c = Answer
678966 mod p = 6a + 6b + 9c + 8a + 7b + 6c = Answer
7 ( 1, 3, 2, -1, -3, -2, cycle goes on. )
Example: 678966 mod 7 = 6 + 3 x 6 + 2 x 9 - 8 - 7 x 3 - 6 x 2 = 1
11 ( 1, -1, cycle goes on. )
Example: 6789 mod 11 = 9 - 8 + 7 - 6 = 2
13 ( 1, 10, -4, -1, -10, 4, cycle goes on. )
Example: 678966 mod 13 = 6 + 6 x 10 - 9 x 4 - 8 - 7 x 10 + 6 x 4 = -24 mod 13 = 2
17 ( 1, 10, -2, -3, 4, 6, -8, 5, -1, -10, 2, 3, -4, -6, 8, -5, cycle goes on. )
67896623 mod 17 = 3 + 2 x 10 - 6 x 2 - 6 x 3 + 9 x 4 + 8 x 6 - 7 x 8 + 6 x 5 = 51 mod 17 = 0
19 ( 1, 10, 5, -7, 6, 3, -8, -4, -2, -1, -10, -8, -11, 5, 4, -6, 9, -2, 3, 7, cycle goes on. )
678966231 mod 19 = 1 + 3 x 10 + 2 x 5 - 6 x 7 + 6 x 6 + 9 x 3 - 8 x 8 - 7 x 4 - 6 x 2 = -42 mod 19 = 15