Given an integer n (n≠0), there are a finite number of sequences of consecutive integers whose terms add up to n (If n=25, then 3+4+5+6+7=25 is one such sequence with 5 terms).

a. Find an equation for the number of terms of the longest such sequence for any positive integer n.

b. Find equations for the bounds (the first and last terms) of the longest such sequence for any positive integer n.

Hint: Once you have an equation for the number of terms, and for the first term of the sequence, the last term is simply one less than their sum.

Hint 2: Ducks have absolutely nothing to do with the problem.

I know, but if n=0 there are in infinite number of such sequences:

-1 + 0 + 1 = 0
-2 + -1 + 0 + 1 + 2 = 0
etc.

(a) specifically states a POSITIVE integer, but the first sentence of the puzzle is in fact false.

All I have for (a) so far is some ugly quadratic equations.....

Posted by Brian Wainscott on 2003-08-04 06:59:21