Given positive integer n, consider the set of numbers {n²+1, n²+2, ... (n+1)²}. If we pick two numbers x and y out of that set, how many different values can the product xy take?
I don't think that anybody has yet posted a proof that the
n(2n+1) products of distinct pairs drawn from the given set are
all distinct. Somebody therefore still needs to show that
if n² < a < b < c < d < (n+1)²+1, then ad=bc is
not possible.
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Posted by Richard
on 2005-08-20 02:00:01 |
Where's the proof?
