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).
Read more about this topic: Amicable Numbers
Famous quotes containing the word regular:
““I couldn’t afford to learn it,” said the Mock Turtle with a sigh. “I only took the regular course.”
“What was that?” inquired Alice.
“Reeling and Writhing, of course, to begin with,” the Mock Turtle replied; “and then the different branches of Arithmetic—Ambition, Distraction, Uglification, and Derision.”
“I never heard of ‘Uglification,’” Alice ventured to say.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)