Monday, January 16, 2006

New Problem Restated

Here's a refinement of the problem. Given fixed integers a, b, and a variable integer x, find for what values of x this equation holds:

ax + b = (2x + 1) + (2x + 3) + ... + (2y - 1) = y^2 - x^2

Unfortunately, the value of y is not known.

The idea is to find out if the equation has solutions by looking at a and b. Factoring each ax + b yields the answer but it takes way too much time. Here's some info.

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