Wednesday, January 11, 2006

New Year, New Problem

I have a new math problem to tackle. For fixed integers a, b and a variable integer x, when is ax + b the sum of consecutive odd integers? Unfortunately the stuff I found (connected with Diophantine equations) is not very helpful, and I couldn't find papers about this issue either. Grrrr...

3 comments:

Anonymous said...

I don't know how you want a solution.
One solution is to test

0 == modulo base 4 ( a * x + b )

or, more precisely,

0 == (a * x + b ) % 4

The consecutive odd integers is a requirement that the total is divisible by four.

Andres said...

Given fixed integers a, b, the problem is to find all values of x such that ax+b = sum of consecutive odd integers.

I don't quite understand your comment, however. For example, you could have 3+5+7=15, and clearly this is not a multiple of 4. Setting a=15 and b=0 yields a solution of x=1... ???...

Andres said...

The idea is to find out without factoring ax + b.