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Under "

**Number System: Formulas, Tips and Tricks to Solve Questions**", we will discuss some important formulas, tips and tricks to easily solve problems based on the number system.**Some important basic formulas :**

- (
*a*+*b*)(*a*-*b*) = (*a*^{2}-*b*^{2}) - (
*a*+*b*)^{2}= (*a*^{2}+ b^{2}+ 2*ab*) - (
*a*-*b*)^{2}= (*a*^{2}+ b^{2}- 2*ab*) - (
*a*+*b*+*c*)^{2}=*a*^{2}+ b^{2}+*c*^{2}+ 2(*ab*+*bc*+*ca*) - (
*a*^{3}+*b*^{3}) = (*a*+*b*)(*a*^{2}-*ab*+*b*^{2}) - (
*a*^{3}-*b*^{3}) = (*a*-*b*)(*a*^{2}+*ab*+*b*^{2}) - (
*a*^{3}+*b*^{3}+*c*^{3}- 3*abc*) = (*a*+*b*+*c*)(*a*^{2}+*b*^{2}+*c*^{2}-*ab*-*bc*-*ac*) - When
*a*+*b*+*c*= 0, then*a*^{3}+*b*^{3}+*c*^{3}= 3*abc*

**Some Basic Things to know before solving number system problems :**

- Dividend = ( Divisor x Quotient ) + Remainder

- If a number n is divisible by two co-primes numbers a, b then n is divisible by ab. In other words, To find a number, say b is divisible by a, find two numbers m and n, such that m*n = a, where m and n are co-prime numbers and if b is divisible by both m and n then it is divisible by a.

- (a-b) always divides (a
^{n}- b^{n}) if n is a natural number.

- (a+b) always divides (a
^{n}- b^{n}) if n is an even number.

- (a+b) always divides (a
^{n}+ b^{n}) if n is an odd number.

**Some Basic Number Series to know :**

- (1+2+3+...+n) = (1/2)n(n+1)
- (1
^{2}+2^{2}+3^{2}+...+n^{2}) = (1/6)n(n+1)(2n+1) - (1
^{3}+2^{3}+3^{3}+...+n^{3}) = (1/4)n^{2}(n+1)^{2} - Sum of the first n odd numbers = n
^{2} - Sum of first n even numbers = n ( n + 1)

**At Last, Thanks for choosing Loud Study.**

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