Some tips in number system

1. The sum of five consecutive whole numbers is always divisible by 5.
2. The product of three consecutive natural numbers is always divisible by 6.
3. The product of three consecutive natural numbers, the first of which is even number is always divisible by 24.
4. For any natural number ‘n’, n³ – n is divisible by 6.
5. Any number written in the form of 10ⁿ – 1, is divisible by 3 or 9, where ‘n’ is natural number.
6. The square odd number when divided by 8 leaves remainder 1.
7. For any prime number P > 3, P² – 1 is divisible by 24.
8. aⁿ + bⁿ is always divisible by a + b, when ‘n’ is odd.
9. aⁿ + bⁿ is never divisible by a – b.
10. aⁿ – bⁿ is exactly divisible by a + b, when ‘n’ is even.
11. aⁿ – bⁿ is exactly divisible by a – b, when ‘n’ is even or odd.
12. The sum of two digit number and number formed by interchanging its digits is always divisible by 11.
13. The difference of two digit number and number formed by interchanging its digits is always divisible by 9