Cambridge Chat (previously New Cambridge Students Entry 2004)

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fishpaste

Are you sure that's a necessary condition for t to be a square?

16 is a square, but neither 8 or 2 are squares.

I'm missing something here lol.

For the 16 situation it won't work. Because, either n is odd, or n+1 is odd.

Reply 4561

fishpaste

Camford

That's why I said I probably missed out on something. From what I remember, the first few numbers in the sequeneces we found gave every number that fit the criteria without missing anything out.

I'll spend sometime on it and see what I can come up with.

Yep it's a much better way to generate them than we've found. I asked Rich last night about it and he pointed me at:

this does seem to look vaguely similar to what you were saying

because like case1:

n = p^2
(n+1)/2 = q^2

p^2 = 2q^2 - 1 = (rt2.q + 1)(rt2.q - 1)

and well if n is an integer, then n^2k is a square, so I can see where that 2n came in. So yeah looks like this is definitely on the right lines

Reply 4562

fishpaste

Camford

For the 16 situation it won't work. Because, either n is odd, or n+1 is odd.

oh yeah

Reply 4563

Camford

fishpaste

Yep it's a much better way to generate them than we've found. I asked Rich last night about it and he pointed me at:

So what does this thing do? Generate n or generate T?

generates T

So what does this thing do? Generate n or generate T?

Never mind, found it on mathworld.

Reply 4566

Camford

fishpaste

generates T

Did you read that article about this square triagular numbers? It didn't take Euler to figure out there are infinte numbers of such number that afternoon.

Reply 4567

fishpaste

Camford

Did you read that article about this square triagular numbers? It didn't take Euler to figure out there are infinte numbers of such number that afternoon.