Before any stones are thrown …the tenuous connection to chess is that a chess board has a square root on it (8x8=64). Figured it needed a relation to chess, no matter how feeble.
Well, let’s see. The last one was 5 years ago, the next one will be in 7 years, and the one after that will be another 9 years down the road. Is there a trend developing?
Bill, you are right. Since
(a + 1)2 - a = 2a + 1, so it doesn’t suprise me the difference between the squares of consecutive integers is an odd number.
Not only that, but 2a + 1 increases by 2 every time a increases by 1, thus proving not only that the differences are all odd, but also that they go up in arithmetic sequence, i.e. 1,3,5,7…