Posted by Denis Borris on September 11, 2002 at 18:15:52:
In Reply to: Re: consecutive numbers posted by Soroban on September 11, 2002 at 13:31:36:
: : Sum of numbers from 1 to A = sum of numbers from A+1 to B.
: : This is an example where A=14 and B=20:
: : 1 + 2 ... + 14 = 105
: : 15 + 16 ... + 20 = 105
B is greater than A; so let X = B - A; then:
2A(A + 1) = (A + X)(A + X + 1)
leads to:
A = [sqrt(8X^2 + 1) + 2X - 1] / 2
I know it's just another way to manipulate, but does it
indicate a Pell equation in an easier "way"?