by Quelloquialism » Fri Oct 26, 2007 5:53 pm
Oh, I forgot the ones that I actually do know, haha:
Deficient numbers are greater than the sum of their proper positive integral divisors; perfect numbers are equal to the sum of their proper positive integral divisors; abundant numbers are less than the sum of their proper positive integral divisors.
The best way to approach these three types, I think, are to memorize a few key numbers and learn a few key concepts:
a) There are only three perfect numbers under 1000; they are 6, 28, and 496.
b) All multiples of perfect numbers are abundant.
c) There are only fourteen abundant numbers under 1000 which cannot be derived from rules a) and b); they are 20, 70, 88, 104, 272, 304, 368, 464, 550, 572, 650, 748, 836, and 945.
d) All multiples of abundant numbers are abundant.
Really, I don't think you'd have to memorize even that many, at least for those abundants in part c)...I wouldn't know how far the tests go, though, because I've never bothered to look too much into it.
I think the only way I'll force myself to remember these is to make a program for generating and analyzing them. That's the only reason I can remember Abundant/Deficient/Perfect, when it was brought up a long time ago in the days when Texasmath used a Bravenet forum.