Counter Examples
Mathematics Dictionary
Dr. K. G. Shih

Keyword - Amicable Numbers
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Program ABH .... Application of Mathematics Dictionary on Web
Subjects

Q1. Hightlight
  • What are amicable pairs ?
  • What two numbers are the first amicable pairs ?
  • Who discovered the amicable pairs ?
  • How to find amicable pairs in Mathematics Dictionary ?
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Q2. What is amicable number ?
A2. 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
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Q3. Can we have more pairs ?
A3. 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
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Q4. Where can we find more ? Reference
A4. Answer
    * P234-235. Computer Mathematics by Dr. K. G. Shih
    * Mathematics Dictionary Program 01 09
    * Mathematics Dictionary Program 01 24
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Q5. What can we learn related with this keyword ?
A5. 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
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Q6. How to find Amicable number from Mathematics Dictionary ?
A6. Answer
    * You should download MD2002 to run on your computer
    * You can find it in chapter 1 program 09 or 24
    * You can find it by keyword Amicable in index
    * You can find it by keyword Amicable in text file ZA.txt
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Q7. Is there sample on internet ?
A7. Answer Amicable number sample from software MD2002
Reference
  • Amicable number : MD2002 ZM01 program 09 or 24
  • Amicable number : Computer Mathematics by Dr Shih, Page 234-235
  • Text file : MD2002 ZA.txt
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Q8. Reference
  • Amicable number : MD2002 ZM01 program 09 or 24
  • Amicable number : Computer Mathematics by Dr Shih, Page 234-235
  • Text file : MD2002 ZA.txt
 Go to Begin
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Copyright © Dr. K. G. Shih. Nova Scotia, Canada.
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