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Amicable Numbers

umasundresh 8 Jan 2026 No Comments

Amicable numbers are pairs of positive integers where each number equals the sum of the proper divisors of the other number. Proper divisors are all the positive divisors of a number except the number itself.

The smallest pair of amicable numbers is 220 and 284:

Amicable numbers may not appear in everyday calculations, but they play an important role in mathematics. They help us understand how numbers relate through their factors and divisors, sharpen pattern recognition, and build strong logical thinking. Often used in number theory, teaching, and programming practice, amicable numbers remind us that some parts of mathematics exist not for direct application, but to train the mind to think clearly and deeply.

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Math titbits

umasundresh 9 Mar 2023 No Comments

For example:

If we consider the three consecutive numbers 7,8 and 9

8² = 64

7 X 9 = 63.

ALGEBRA Applications Number theory

Suitcase lock problem

umasundresh 25 Jan 2023 No Comments

You have recently purchased a suitcase that features a combination number lock. Each slider provides a selection of ten numbers, ranging from 0 to 9. In order to prevent anyone from opening your suitcase, you will need to come up with a secret number combination. Do you know how many different possible choices there are for secret codes?

Solution:

You have an option of ten different digits, ranging from zero to nine, for each of the digits in the slider.

Therefore, the number of different combinations that can be made are

10 X 10 X 10 = 1000 options.

If there is a condition that the digit in the slider should not be repeated, then the following applies:

You will have a choice of 10 numbers for the first slider, and 9 for the second slider and 8 for the third slider.

Which means, we have

10 X 9 X 8 = 720 options.

The following video will explain the given problem:

Number theory

Happy Pi day!!!

umasundresh 14 Mar 2022 No Comments

Mathematicians Number theory

Kaprekar constant

umasundresh 10 Mar 2022 No Comments

The number 6174 is called the Kaprekar constant. It was discovered by the Indian Mathematician Kaprekar.

We get this constant if we perform certain routine calculations to any four-digit number.

The rule is

1. Take any 4 digit number.

2. Arrange the digits of the 4 digit number in descending and ascending order.

3. Subtract the smaller number from the bigger number

4. Repeat the steps from 2 for the answer obtained also.

Repeat the steps till you reach 6174.

We always end up with 6174. Once you reach 6174, the process will continue generating the same number.

Let us solve an example to understand this..

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Kaprekar Number

umasundresh 9 Mar 2022 No Comments

A Kaprekar number is

A number’s square divided into two parts such that the sum of its parts is equal to the original number.

Kaprekar Number

An example of this Kaprekar Number is explained in the following video.

Mathematicians Number theory

D.R.Kaprekar

umasundresh 17 Feb 2022 No Comments

D.R.Kaprekar was a Nashik School Math teacher, He discovered several classes of Numbers and constants in the field of Number theory, which are named after him as Kaprekar Number and Kaprekar Constant.

Other discoveries include Self Numbers, Harshad Number and Demlo Number.

He became popular when Martin Gartner wrote about him on his article for ‘Mathematical Games for Scientific Americans’.

ALGEBRA Number theory

Cool math titbits

umasundresh 23 Dec 2021 No Comments

Mathematicians Number theory

National Mathematics Day

umasundresh 22 Dec 2021 No Comments

December 22 is celebrated as the National Mathematics Day in honor of the birth anniversary of Indian Mathematical genius Srinivasa Ramanujan.

math facts Mathematicians Number theory

Ruth-Aaron Pair

umasundresh 21 Dec 2021 No Comments

Ruth-Aaron pair consists of consecutive numbers such that the sum of their prime factors are equal.

grayscale photo of man in baseball uniform standing on field

Ruth and Aaron are baseball players. Aaron scored 715 home runs and broke the previous record of 714 home runs held by Ruth.

The name Ruth-Aaron pair was given by Carl Pomerance. It was first noticed and solved by his colleague’s student.

The prime factors of 715 and 714 are as follows,

715 = 2 X 3 X 7 X 17

714 = 5 X 11 X 13

The sum of the prime factors of both the numbers is 29 respectively.

The mathematicians Carl Pomerance and his colleagues Carol Nelson and David.E.Penny tried to find more Ruth-Aaron pairs, Some of the few examples are given below

5 and 6

5 = 5

6 = 2 X 3

2 + 3 =5

2. 8 and 9

8 = 2 X 2 X 2

9 = 3 X 3

2 + 2 + 2 = 3 +3 = 6

3. 15 and 16

15 = 3 X 5

16 = 2 X 2 X 2 X 2

3 + 5 = 2 + 2 + 2 + 2 = 8

4. 77 and 78

77 = 7 X 11

78 = 2 X 3 X 13

7 +11 = 2 +3 + 13 =18

5. 714 and 715

715 = 2 X 3 X 7 X 17

714 = 5 X 11 X 13

2 +3 + 7 + 17 = 5 + 11 + 13 = 29

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Amicable Numbers

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