What is special about these two numbers: 220 and 284?

  • Thread starter Greg Bernhardt
  • Start date
  • Tags
    Numbers
In summary, the numbers 220 and 284 are amicable numbers, meaning that they are a pair of numbers where each number is the sum of the proper divisors of the other number. They were discovered by the Pythagorean philosopher Nicomachus in the 2nd century AD and have been studied by mathematicians throughout history. There are many other pairs of amicable numbers, and they are considered special because of their unique relationship and interesting mathematical properties. Amicable numbers have applications in various areas of mathematics and have led to the discovery of other types of special numbers.
  • #1
19,412
9,961
What is extremely special about these two numbers: 220 and 284? They are ______ pairs.
 
Physics news on Phys.org
  • #2
There amicable pairs. Adding all the divisors of 220 gives you the number 284
 
  • #3
point for Robert Zaleski!
 

1. What is the significance of the numbers 220 and 284?

The numbers 220 and 284 are known as amicable numbers, meaning that they are a pair of numbers where each number is the sum of the proper divisors of the other number. In this case, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, which add up to 284. Similarly, the proper divisors of 284 are 1, 2, 4, 71, and 142, which add up to 220.

2. How were these numbers discovered?

The discovery of amicable numbers dates back to ancient Greece, but the specific pair of 220 and 284 was first recorded by the Pythagorean philosopher Nicomachus in the 2nd century AD. They were later studied by other mathematicians, including the famous mathematician Leonhard Euler in the 18th century.

3. Are there other pairs of amicable numbers?

Yes, there are many other pairs of amicable numbers. In fact, it is estimated that there are over 1 million pairs of amicable numbers, although only a few hundred have been discovered so far. The smallest known pair is 220 and 284, and the largest known pair is 9,363,584,538,952,064, and 9,437,265,624,385,600.

4. What makes these numbers special?

The main reason these numbers are considered special is because of their unique relationship as amicable numbers. They also have some interesting mathematical properties, such as being part of a set of numbers called perfect numbers, which are numbers that are equal to the sum of their proper divisors.

5. How are amicable numbers used in mathematics or science?

Amicable numbers have been studied and used in various areas of mathematics, including number theory, algebra, and geometry. They also have applications in cryptography and coding theory. In addition, the study of amicable numbers has led to the discovery of other types of special numbers, such as sociable numbers and perfect numbers.

Similar threads

  • General Discussion
Replies
4
Views
734
  • General Discussion
Replies
16
Views
1K
  • Electrical Engineering
Replies
5
Views
995
  • General Discussion
Replies
2
Views
921
Replies
4
Views
687
  • General Discussion
2
Replies
43
Views
4K
  • General Math
Replies
13
Views
3K
  • General Discussion
Replies
19
Views
2K
Replies
17
Views
887
  • General Discussion
Replies
5
Views
869
Back
Top