Alright I cheated bit, ok? I'm a cheater by nature. I started cheating since the age of 8. Now I am very experienced cheater, I think I probably cheated my way through the Dec interview into Cambridge.
[UK, perh. originally from the first "Roger Irrelevant" strip in "VIZ" comics] 1. n.,v. Commonly used to describe chatter, content-free remarks or other essentially meaningless contributions to threads in newsgroups. "Oh, rspence is wibbling again". 2. [UK IRC] An explicit on-line no-op equivalent to humma. 3. One of the preferred metasyntactic variables in the UK, forming a series with 'wobble', 'wubble', and 'flob' (attributed to the hilarious historical comedy "Blackadder"). 4. A pronounciation of the letters "www", as seen in URLs; i.e., www.foo.com may be pronounced "wibble dot foo dot com" (compare dub dub dub).
I know. I could have done better at school if I didn't think about cheating all that much... *Camford is ashamed of himself.*
Hehe, I wasn't having a go at you. I just always like to solve stuff myself...my physics teacher actually used the problem to allow us to work out his house number so that we could go to a dinner he was hosting. I suppose I could've just looked him up in the phone directory, but it would've taken the fun out of it.
Find an general equation, or groups of equations which describe numbers which are triangle numbers as well as square number. If you it's the latter, please states starting values.
8p^2 + 1 is an odd square. if you can generate such p, the p(p+1)/2 will be a triangular square, but I can't generate 8p^2 + 1 which are odd squares
*edit* just seen that 8p^2 + 1 is always odd because 8p^2 is clearly odd so +1 makes it odd. so the "odd" part is redundant
so basically if you could solve
8p^2 + 1 = q^2
you could generate triangular squares. like consider p = 1, the expression is consistent for integers (with q = 3), then p(p+1)/2 = 1 which is a triangular number
or p = 6 ... (makes q = 17)
p(p+1)/2 = 6*7/2 = 21 ...which is another triangular number
Shouldn't we take this elsewhere before this thread is moved to the Maths forum?
If you get some mathematicain to analyse this thread, it has got less than 50% of mathematical contents in it. Therefore, this thread can not be dubbed as a mathematics thread in principle. Which means we are safe. Beside, we are all going to Cambridge next year.
8p^2 + 1 is an odd square. if you can generate such p, the p(p+1)/2 will be a triangular square, but I can't generate 8p^2 + 1 which are odd squares
A friend (going Christ but don't use UKL) and I spent about 40 mins on this problem during a maths lesson 3 months ago. We managed to get two sequences of numbers which generate numbers that fit the criteria of the quetions when put into a equation. But, unfortunately, I lost the sheet of paper to my beloved bin bag after the lesson. So, now, I'm just as clueless as you are, mate.