To expand on that last paragraph: If x is the smallest coefficient, it makes sense that once you find x number of consecutive solutions, you will have ability to create all solutions after that, since doing so merely requires that you add x to each of the previous solutions. Whether you need at leastx number is what I haven't formally proven, but using an equation where the smallest coefficient is greater than 6 and the largest one is relatively large by comparison shows that it requires more than 6 consecutive solutions to find the last number that doesn't have one.
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branchandroot
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Date: 2010-01-27 03:49 pm (UTC)To expand on that last paragraph: If x is the smallest coefficient, it makes sense that once you find x number of consecutive solutions, you will have ability to create all solutions after that, since doing so merely requires that you add x to each of the previous solutions. Whether you need at least x number is what I haven't formally proven, but using an equation where the smallest coefficient is greater than 6 and the largest one is relatively large by comparison shows that it requires more than 6 consecutive solutions to find the last number that doesn't have one.