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THE END OF AN ERA

*This article was written on 14th March 2018, the day when legendary Astrophysicist Stephen Hawking passed away.  The 14th of march marks the birth anniversary of the legendary physicist Albert Einstein. Stephen Hawking leaving us on this very day is quite symbolic and coincidental. Once we accept our limits, we go beyond them. -  Albert Einstein The 14th of march marks the birth anniversary of the legendary physicist Albert Einstein. Stephen Hawking leaving us on this very day is quite symbolic and coincidental. We know Stephen hawking not only as a physicist but also as a man who really went to the next level to unravel the mysteries of nature. Not only did his work in theoretical physics and cosmology change our way of looking at the universe, but the way he lived his life changed our mindset of looking towards our lives as well. He put forward the concept of radiation emitted by a black hole, now known as the Hawking radiation. We all know him as the author of the best-selling book
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On the solutions of an equation.

                                                       Kunal A. Borse      I will start with a little anecdote from the life of mathematician Srinivasa Ramanujan. Once a friend visited him, while Ramanujan was cooking in his kitchen. His friend was solving a puzzle from the 'Strand' magazine, but he just could not crack it. So he read it out to Ramanujan. The puzzle goes as follows-    'Find the numbers x and y, given that                              1+2+3+......+(x-1)+x=x+(x+1)+.....+y and 50<y<500.'   Much to his friend's amusement, Ramanujan, still busy with his cooking, answered correctly within a moment. "The value of y must be 288 while that of x must be 204,''  said Ramanujan, leaving his friend surprised. This shows how much Ramanujan was 'into' numbers and thought about numbers all the time.        Now let us look at this problem and try to find more such pairs of numbers, because this sure looks like a very inter
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The Weirdest coincidence.

The Weirdest coincidence . Kunal .A. Borse      While thinking about the ‘Kaprekar constant (6174) ’, I came across another constant. The following constant is defined for a four digited number. The process to be followed is described below. We take a random four digited number, say ‘abcd’ (in decimal form). Then we arrange its digits in an ascending and descending order, and divide both these into two 2 digited numbers, and perform the following. Let a>b>c>d without loss of generality, abcd -ab and cd dcba- dc and ba We calculate       (ab)^2 +(cd)^2 – (dc)^2 – (ba)^2 We do the process again after getting the result until we keep getting the same result. On getting a three digited number, we consider it to be four digited by adding a zero to the left. What I observed was that we always get the number 1782 or 0 after performing this operation. It is quite easy to see that 1782 again gives 1782 on subjected to this process. I checked this using a C prog
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