# Number System : Formulas, Tips and Tricks to Solve Questions

Hello friends!

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 :
1. (a + b)(a - b) = (a2 - b2)
2. (a + b)2 = (a2 + b2 + 2ab)
3. (a - b)2 = (a2 + b2 - 2ab)
4. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
5. (a3 + b3) = (a + b)(a2 - ab + b2)
6. (a3 - b3) = (a - b)(a2 + ab + b2)
7. (a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
8. When a + b + c = 0, then a3 + b3 + c3 = 3abc

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 (an - bn) if n is a natural number.
• (a+b) always divides (an - bn) if n is an even number.
• (a+b) always divides (an + bn) if n is an odd number.
Some Basic Number Series to know :
1. (1+2+3+...+n) = (1/2)n(n+1)
2. (12+22+32+...+n2) = (1/6)n(n+1)(2n+1)
3. (13+23+33+...+n3) = (1/4)n2(n+1)2
4. Sum of the first n odd numbers = n2

5. Sum of first n even numbers = n ( n + 1)
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