Monday, April 9, 2018

Brahmagupta - Fibonacci Identity


                                                      Brahmagupta - Fibonacci Identity 


There is a very famous identity used in algebra known as – Brahmagupta – Fibonacci identity that expresses the product of two sums of two squares as a sum of two squares in two different ways.
                        (a2 + b2) (c2 + d2) = (ac – bd)2 + (ad + bc)2      
                                                  = ( ac + bd)2 + (ad – bc)2
For example:-
(12 + 42) (22 + 72) = (2 – 28)2 + (7 + 8)2
                            = 262 + 152
And
(12 + 42) (22 + 72) = (2 + 28)2 + (7 – 8)2
                            = 302 + 12


Dr Rajesh Kumar Thakur

Wednesday, April 4, 2018

Mathematically 101

                                                               101

1. One hundred one is a sexy prime as well as a sexy prime triplet. Sexy primes differ from each other by 6. If p is a prime and p + 6 is also a prime then it is called a sexy prime.
Example:- (5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107)

2. 101 is also a sexy prime triplet. If p, p+6 and p + 12 are all prime then it is called sexy prime triplet.
Example:- (5,11,17), (7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113),

3. It is the sum of 5 consecutive primes
                                       13 + 17 + 19 + 23 + 29 

4. It can be written as the sum of first 5 factorial with alternate sign.
                                  101 = 5! - 4! + 3! - 2! + 1!

5. It is a palindrome number and a palindrome prime.

6. It is the largest prime in form of 10^n + 1
                                   101 = 10^2 + 1

7. There are 101 digits in the product of the 39 successive primes produced by the formula n2 + n + 41, where n = 1 to 39. This formula was used by Charles Babbage to demonstrate the capabilities of his Difference Engine (1819-1822))

Happy reading 
Dr Rajesh Kumar Thakur

List of Some Interesting Numbers