My Integer Factorization Study: Avenues Inspired by the New Chart


Goal: Given odd positive integer m , its ceiling square c, and the remainder r=c2-m, determine the column x and row y in the previously posted chart at which m is located. The range of integers between (c-1)2 and c2 falling on the upper half of one of the diagonals holding consecutive values and the lower half of the next one, this should be an easy task. Now that I am typing about it, I actually think I might have that formula tonight. Mind you, how helpful it will be for the factorization of an arbitrary m, I don’t yet know. Let’s just see what the x and y turn out to be… and what they do with row polynomials expressed only in terms of x, and column polynomials only in terms of y … I think.

Stay tuned!

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