##### NUMBERS-SPECIALITY

**Automorphic number :**

An automorphic number is a number which is present in the last digit(s) of its square. Example: **25** is an automorphic number as its square is **625** and **25** is present as the last digits.

**Neon number:**

A number is said to be a **Neon Number** if the sum of digits of the square of the number is equal to thenumber itself. Example 9 is a **Neon Number**. 9*9=81 and 8+1=9.Hence it is a **Neon Number**.

**Magic number** :

A number is said to be a **Magic number** if the sum of its digits are calculated till a single digit is obtained by recursively adding the sum of its digits. If the single digit comes to be 1 then the number is a **magic number**.

Example :

**901**

**9+0+1=10**

**1+0=1**

*Palindrome:*

Reverse of a number is also same as the original number.

Examle:

**100001,**

**123454321.**

T**axicab number:**

In mathematics, the *n*th **taxicab number**, typically denoted Ta(*n*) or Taxicab(*n*), also called the *n*th **Hardy–Ramanujan number**, is defined as the smallest number that can be expressed as a sum of two *positive* cube numbers in *n* distinct ways. The most famous taxicab number is 1729 = Ta(2) = 1^{3} + 12^{3} = 9^{3} + 10^{3}.

**Armstrong number:**

A positive integer is called an *Armstrong number* of order n if abcd… = a^{n} + b^{n} + c^{n} + d^{n} + … In case of an *Armstrong number* of 3 digits, the sum of cubes of each digits is equal to the *number* itself. For example: 153 = 1*1*1 + 5*5*5 + 3*3*3 // 153 is an *Armstrong numbe**r*.

**Strong number**:

If the sum of factorial of the digits in any number is equal the given number then the number is called as STRONG number.

Ex=1! +4! +5!= 1+24+120 = 145

**Perfect Number:**

In number theory, a **perfect number** is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself

Ex: 6 (1,2,3,6 sum of divisors excluding itself=1+2+3=6)

**Happy number:**

A *happy number* is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process **ends in 1 are happy numbers**, while those that **do not end in 1 are unhappy numbers** (or sad numbers).