Find all series of consecutive positive integers whose sum is exactly 10,000.
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What if we don't require the consecutive integers to (all) be positive?

Amazingly, we have just dealt with this same subject in a recent perplexus puzzle.  See for example http://perplexus.info/show.php?pid=2030&cid=15599 . 10,000 has 5 odd divisors and thus there are 5 easily-found (Riley's method) representations of 10,000 as a sum of consecutive positive integers, including the trivial representation with just one term. Allowing negative integers to appear additionally allows a representation that contains negative terms for each representation with only positive terms.

Edited on July 21, 2004, 1:53 pm

Posted by Richard on 2004-07-21 12:49:03