Mathematics Dictionary Dr. K. G. Shih Keyword - Amicable Numbers

Index .......... Contents of Mathematics Dictionary by index Sections ....... Contents of Mathematics Dictionary by chapters Program ABI .... Application of Mathematics Dictionary on Web

Q1 : What is amicable number ? Answer * The sum of factors of 1st number = 2nd number. * The sum of factors of 2nd number = 1st number. * Then these two numbers are called amicable pairs [Example] 220 and 284 are amicable pairs. [Example] 1 + 2 + 4 + 71 + 142 = 220 [Example] Prove that sum of factors of 220 = 284 Q2 : Can we have more pairs ? Answer : Pairs between 1000 and 10000 are 1184 and 1210 2620 and 2924 5052 and 5564 6232 and 6368 Reference : p234-p235 Computer Math by Dr shih Reference : Mathematics Dictionary Chapter 1 program 9 and 24 Q3 : Where can we find more ? Reference * P234-235. Computer Mathematics by Dr. K. G. Shih * Mathematics Dictionary Program 01 09 * Mathematics Dictionary Program 01 24 Q4 : What can we learn related with this keyword ? Answer * Euler (1707-1783) discovered 59 amicable number pairs * If sum of factors = number itself, it is a perfect number * 1st perfect number is 6 * 2nd perfect number is 28 * 3rd perfect number is 496 [Example] 1,2,3 are factors of 6 and 1+2+3=6 Is is 1st perfect number Prove that 28 is the 2nd perfect number Prove that 496 is the 3rd perfect number What is the 4th perfect number ? See keyword Perfect number in Math Dictionary Q5 : How to find Amicable number from Math Dictionary ? Answer * You should download MD2002 to run on your computer * You can find it in chapter 1 by Program ABD * You can find it by keyword Amicable in Program ABCE > * You can find it by keyword Amicable in Program ABE * MD2002 is simple in use : * E.g. Use Program ABC : Click Text A and Click Amicalbe * E.g. Use Program ABD : Chapter 1 and program 9 * E.g. Use Program ABE : Find Amicable in index and click it Q6 : Amicable sample from software MD2002 Mathematics Dictionay Dr. K. G. shih 11 Lantana Terrace, Dartmouth, NS, Canada. B2X 3L3 phone .......... (902) 434 1981 email .......... kshih@hfx.eastlink.ca URL ............ http://geocities.com/b192907 Webpage ........ Mathematics Dictionary