Do You Know?

1. What is so special abount numebr 3?

2. What are Amicable numbers?

Amicable numbers are a pair of numbers with the following property: the sum of all of the proper divisors of the first number (not including itself) exactly equals the second number while the sum of all of the proper divisors of the second number (not including itself) likewise equals the first number.

For example let's show that 220 & 284 are amicable numbers:
First we find the proper divisors of 220:

1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110

If you add up all of these numbers you will see that they sum to 284.

Now find the proper divisors of 284:

1, 2, 4, 71, 142

These sum to 220, and therefore 220 & 284 are amicable numbers.

Try to find other Amicable number............

3. What is special about number 1729?

1729 is the smallest number that is expressable as the sum of two distinct squares in two different ways

1729= 1³ + 12³ = 9³ + 10³

4. Number 666 is called as Number of Beast ....Why so

The number 666 is a simple sum and difference of the first three 6th powers:

666 = 1³ - 2³ + 3³.

It is also equal to the sum of its digits plus the cubes of its digits:

666 = 6 + 6 + 6 + 6³ + 6³ + 6³.

666 is related to (6² + n²) in the following interesting ways:

666 = (6 + 6 + 6) · (6² + 1²)
666 = 6! · (6² + 1²) / (6² + 2²)

The sum of the squares of the first 7 primes is 666

The sum of the first 144 (= (6+6)·(6+6)) digits of pi is 666.

A very special kind of prime number is a prime, p (that is, let's say, the kth prime number) in which the sum of the decimal digits of p is equal to the sum of the digits of k. The beastly palindromic prime number 16661 is such a number, since it is the 1928'th prime, and

The triplet (216, 630, 666) is a Pythagorean triplet, as pointed out to me by Monte Zerger. This fact can be rewritten in the following nice form:

There are only two known Pythagorean triangles whose area is a repdigit number: