Number System : Formulas, Tips and Tricks to Solve Questions

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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 :

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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