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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