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