If n is a positive integer, then 3 (n + 2) - 3 (n) can be divided by 24

If n is a positive integer, then 3 (n + 2) - 3 (n) can be divided by 24

3^(n+2)-3^n
=3^n(9-1)
=3^n*8
=3^(n-1)*3*8
=3^(n-1)*24
So it's divisible by 24

Find the largest positive integer n, so that N3 + 100 can be divided by N + 10

To make (N3 + 100) / (n + 10) = N3 + 100N + 10 = (n + 10) (n − 10) 2 − 900N + 10 = (N-10) 2-900n + 10 an integer, 900 must be divisible by N + 10, then the maximum value of n is 890

It shows that (n + 14) 2-n2 can be divided by 28

（n+14)²-n²
=(n+14+n)(n+14-n)
=14×(2n+14)
=28(n+7)
∵ n is an integer
N + 7 is an integer
(n + 14) 2-n2 can be divisible by 28