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- n(n + 1)(2n + 1) is always divisible by 6.
- 32n leaves remainder = 1 when divided by 8
- n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9
- 102n + 1 + 1 is always divisible by 11
- n(n2– 1) is always divisible by 6
- n2+ n is always even
- 23n-1 is always divisible by 7
- 152n-1 +1 is always divisible by 16
- n3 + 2n is always divisible by 3
- 34n – 4 3n is always divisible by 17
- n! + 1 is not divisible by any number between 2 and n.(where n! = n (n – 1)(n – 2)(n – 3)…….3.2.1).
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