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| | Square Triangular Numbers (Site not responding. Last check: 2007-10-26) |
 | | The triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45,... |
 | | A standard problem in elementary number theory is to determine ALL the numbers that are both square and triangular. |
 | | So, we've shown that n[k] is a square for every odd index k=2j-1, and of course the quantity 4n is a square if and only if n is a square, so we have the related result that the number 4 n[2j-1] = (3+2sqrt(2))^(2j-1) + (3-2sqrt(2))^(2j-1) - 2 is a square for every positive integer j. |
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