interesting maths results
by Francis[ Edit ] 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 ==> 3
2*3 = 3
6 = 729 / 8 => remainder 1
4) n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9
Example
n = 4 ==> 4
3 + (4 + 1 )
3 + (4 + 2 )
3 = 64 + 125 + 216 = 405 / 9 = 45
5) 102n + 1 + 1 is always divisible by 11
Example
n = 2 ==> 10
2 * 2 + 1 + 1 = 10
5 + 1 = 100000 + 1 = 100001 / 11 = 9091
6) n(n2 - 1) is always divisible by 6
Example
n = 5 ==> 5(5
2 - 1) = 5*(25 - 1 ) = 5*24 / 6 = 20
7) n2 + n is always even
Example
n = 5 ==> 5
2 + 5 = 25 + 5 = 30 (Even)
8 ) 23n - 1 is always divisible by 7
Example
n = 5 ==> 2
3*5 - 1 = 2
15 - 1 = 32768 - 1 = 32767 / 7 = 4681
9) 152n-1 + 1 is always divisible by 16
Example
n = 2 ==> 15
2*2-1 + 1 = 15
3 + 1 = 3375 + 1 = 3376 / 16 = 211
10) 34n - 43n is always divisible by 17
Example
n = 2 ==> 3
8 - 4
6 = 6561 - 4096 = 2465 / 17 = 145
11) n3 + 2n is always divisible by 3
Example
n = 4 ==> 4
3 + 2 * 4 = 64 + 8 = 72 / 3 = 24
