Amicable Numbers - Regular Pairs

Regular Pairs

Let (m, n) be a pair of amicable numbers with m<n, and write m=gM and n=gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair (m, n) is said to be regular, otherwise it is called irregular or exotic. If (m, n) is regular and M and N have i and j prime factors respectively, then (m, n) is said to be of type (i, j).

For example, with (m, n) = (220, 284), the greatest common divisor is 4 and so M = 55 and N = 71. Therefore (220, 284) is regular of type (2, 1).

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Famous quotes containing the word regular:

    The solid and well-defined fir-tops, like sharp and regular spearheads, black against the sky, gave a peculiar, dark, and sombre look to the forest.
    Henry David Thoreau (1817–1862)