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

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

Never mind, found it on mathworld.
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.
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.

Did we?
fishpaste
Did we?

We as in my friend and I.
Camford
We as in my friend and I.

Ahh yes. Sorry =P
fishpaste
Ahh yes. Sorry =P

Are you going to follow my lead and have another go at it or not?
Can't you lot go and have a little mathematician's huddle in a corner somewhere? And stop making the rest of us look stupid?
Helenia
Can't you lot go and have a little mathematician's huddle in a corner somewhere? And stop making the rest of us look stupid?

Did you know Tinky Winky is a gay role model?
Squishy
Did you know Tinky Winky is a gay role model?

The purple one?
lol whatever!

i just have changed my profile pic to one of me WITHOUT my brace! <--like this
Helenia
Can't you lot go and have a little mathematician's huddle in a corner somewhere? And stop making the rest of us look stupid?

*Camford gives Squishy a warm cuddle in the Mathematicians' corner....(manly cuddle, nothing else)*
Squishy
Did you know Tinky Winky is a gay role model?

Of course. Dont you think the poncho and sombrero help?
Helenia
Of course. Dont you think the poncho and sombrero help?

and the dalmation print handbag!
Tinky Winky's too fat to be gay. Everybody knows gay people have rippling six packs.
fishpaste
Tinky Winky's too fat to be gay. Everybody knows gay people have rippling six packs.

Oi, he's a teletubby. Normal rule does not apply.