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Re^2: Triangle Numbers

by Anonymous Monk
on Dec 03, 2005 at 21:56 UTC ( [id://513862]=note: print w/replies, xml ) Need Help??


in reply to Re: Triangle Numbers
in thread Triangle Numbers

I'm looking at triangular and tetrahedral numbers for a paper for my Computational Number Theory class. If you look at how many triangular numbers (1/2*n*(n+1) n in N) are tetrahedral numbers (1/6*n*(n+1)*(n+2) n in N) you find that there are only 5. 5?!?! Everyone I've talked to thought there would be an infinite number of them. But why restrict ourselves to 3-d? Given any number n in a dimension d we can find the d-th dimensional analogue of the n-th triangular number given by binomial(n+d-1, d). Then things start to get strange... Robert Weston OSU Math Major westonr at onid dot orst dot edu

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