Basic Number Theory

• Square of every even Number = An even Number

• Sum of first ‘n’ natural numbers = {n(n+1)}/2

• Sum of first ‘n’ odd numbers = n²

• Sum of first ‘n’ even numbers = n(n+1)

• Sum of square of first ‘n’ natural numbers = {n(n+1)(2n+1)}/6

• Sum of cubes of first ‘n’ natural numbers = {n(n+1)/2}²

• There are 15 prime numbers between 1 & 50 and 10 prime numbers between 50 & 100

• If n divides p & q, then n divides their sum and difference also

      Like: 6 divides 12 & 18, then 12+18 = 30 and 18-12 = 6 are also divided by 6

• For any natural number n, (n³ – n) is divisible by 6

• The product of three consecutive natural numbers is always divisible by 6

• (x^m – a^m) is divisible by (x – a) for all values of m

• (x^m – a^m) is divisible by (x + a) for even values of m

• (x^m + a^m) is divisivlke by (x + a) for odd values of m

• Number of prime factors of a^p b^q c^r d^s is p+q+r+s, where a, b, c, d are prime numbers