# interesting maths results

#### by Francis 2013-06-07 15:03:10

Interesting Maths Results
Some interesting maths calculation and results to made formula.

1) n! + 1 is not divisible by any number between 2 and n

Example
n = 5 ==> 5! + 1 = 120 + 1 = 121 (121 is not divisible by between 2 and 5)

2) n(n + 1)(2n + 1) is always divisible by 6.

Example
n = 2 ==> 2*(3)*(5) = 30 / 6 = 5

3) 32n leaves remainder = 1 when divided by 8

Example
n = 3 ==> 32*3 = 36 = 729 / 8 => remainder 1

4) n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9

Example
n = 4 ==> 43 + (4 + 1 )3 + (4 + 2 )3 = 64 + 125 + 216 = 405 / 9 = 45

5) 102n + 1 + 1 is always divisible by 11

Example
n = 2 ==> 102 * 2 + 1 + 1 = 105 + 1 = 100000 + 1 = 100001 / 11 = 9091

6) n(n2 - 1) is always divisible by 6

Example
n = 5 ==> 5(52 - 1) = 5*(25 - 1 ) = 5*24 / 6 = 20

7) n2 + n is always even

Example
n = 5 ==> 52 + 5 = 25 + 5 = 30 (Even)

8 ) 23n - 1 is always divisible by 7

Example
n = 5 ==> 23*5 - 1 = 215 - 1 = 32768 - 1 = 32767 / 7 = 4681

9) 152n-1 + 1 is always divisible by 16

Example
n = 2 ==> 152*2-1 + 1 = 153 + 1 = 3375 + 1 = 3376 / 16 = 211

10) 34n - 43n is always divisible by 17

Example
n = 2 ==> 38 - 46 = 6561 - 4096 = 2465 / 17 = 145

11) n3 + 2n is always divisible by 3

Example
n = 4 ==> 43 + 2 * 4 = 64 + 8 = 72 / 3 = 24