Integer Factorization: Brief Remainder Line Observation


The slope and y-intercept of the Remainder Line for an odd integer m=c2-r with Ceiling Square c2 and Remainder r on the Zone Grid increase linearly over all values of m having the same r, according to their c value.

This is something I’ve already programmed in to It calculates the Remainder Line coefficients quickly based on c and r. However, my current working spreadsheet of c vs. r, with notations for the Ascents of each m value, makes this relationship much more evident and less random-looking.

In each shaded cell, m is the leftmost number, followed by m’s Ascent(s).

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