Formula for automorphic number?

Asked by: Tyrell Macejkovic
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An n-digit number is said to be automorphic if the last n digits of its square are the same as the original number. For instance, 52 = 25, 62 = 36, 252 = 625, 762 = 5776 and many others.

What are Automorphic numbers in maths?

In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base. whose square "ends" in the same digits as the number itself.

What is an example of automorphic number?

definition and examples

An automorphic number is an integer whose square ends with the given integer, as (25)2 = 625, and (76)2 = 5776. Strobogrammatic numbers read the same after having been rotated through 180°; e.g., 69, 96, 1001.

What is a special number?

If the sum of the factorial of digits of a number (N) is equal to the number itself, the number (N) is called a special number.

25 related questions found

What is a happy number in math?

To find out if a number is happy, replace the number by the sum of the squares of its digits. Repeat the process until either the number equals 1 or loops endlessly in a cycle that does not include 1. When the process ends with 1 then the number is described as a happy number, otherwise, it is an unhappy number.

Is 5 an automorphic number?

An automorphic number is a number whose square ends with the number itself. For example, 5 is an automorphic number, 5*5 =25. The last digit is 5 which same as the given number. It has only a positive single digit number.

What is strong number?

Strong number is a special number whose sum of the factorial of digits is equal to the original number. For Example: 145 is strong number. Since, 1! + 4! + 5!

Is 51 a Harshad number?

The harshad numbers in base 12 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, ᘔ, Ɛ, 10, 1ᘔ, 20, 29, 30, 38, 40, 47, 50, 56, 60, 65, 70, 74, 80, 83, 90, 92, ᘔ0, ᘔ1, Ɛ0, 100, 10ᘔ, 110, 115, 119, 120, 122, 128, 130, 134, 137, 146, 150, 153, 155, 164, 172, 173, 182, 191, 1ᘔ0, 1Ɛ0, 1Ɛᘔ, 200, ...

What are circular numbers?

The square number of a number ends with the same digits as the number itself. That number is known as automorphic number or circular number.

What is palindrome number?

What is a Palindrome Number? A Palindrome no. is the number that remains the same when its digits get reversed. Ex: 15451, for example: If we take 131 and reverse it then after reversing the number remains the same. Input the number from the user.

Is 6 an amicable number?

Amicable numbers are two different numbers related in such a way that the sum of the proper divisors of each is equal to the other number. The smallest pair of amicable numbers is (220, 284). ... For example, the proper divisors of 6 are 1, 2, and 3.)

What is automorphic number in Python?

A number is said to be an automorphic number if the last digits of the square of this number give the same number. Output - Yes, it is an automorphic number. Reason - The square of 25 gives 625, since the last digits are 25 it is an automorphic number.

What is autotrophic number?

In mathematics, an automorphic number is a number whose square "ends" in the same digits as the number itself. For example, 52 = 25, 62 = 36, 762 = 5776, and 8906252 = 793212890625, so 5, 6, 76 and 890625 are all automorphic numbers.

What are neon numbers?

A neon number is a number where the sum of digits of square of the number is equal to the number. The task is to check and print neon numbers in a range. Examples: ... Input :12 Output : Not a Neon Number Explanation: square is 12*12 = 144 and sum of the digits of the square is 9 (1 + 4 + 4) which is not equal to 12.

Is 4 A strong number?

Factorial implies when we find the product of all the numbers below that number including that number and is denoted by ! (Exclamation sign), For example: 4! = 4x3x2x1 = 24. ... Now we will sum up 1 + 24 + 120 so we get 145, that is exactly same as the input given, So we can say that the number is strong number.

How do you check if a number is a strong number?

A number can be said as a strong number when the sum of the factorial of the individual digits is equal to the number. For example, 145 is a strong number. Let's understand through an example. Program to check whether the number is strong or not.

How do I find my Pronic number?

Algorithm to find Pronic Number
  1. Check number N is pronic or not.
  2. Calculate the square root K of the given number N.
  3. Multiply K * (K+1), if result is equal to the number N, then N is a pronic number otherwise not.

Is perfect number Java?

Perfect Number in Java

Any number can be a Java Perfect Number if the sum of its positive divisors excluding the number itself is equal to that number. For example, 28 is a perfect number because 28 is divisible by 1, 2, 4, 7, 14 and 28 and the sum of these values is 1 + 2 + 4 + 7 + 14 = 28.

Who invented Automorphic numbers?

Poincaré on discovery and his work on automorphic functions

One of Poincaré's first discoveries in mathematics, dating to the 1880s, was automorphic forms.

What is the happiest number?

Defined the happiest number as the smallest number that finds the most other happy numbers with it, i.e. 7 found four other numbers (49, 97, 130, and 10) making it a rank 4 in happiness.

Is 21 a happy number?

The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, ... (OEIS A007770). These are also the numbers whose 2-recurring digital invariant sequences have period 1.

What is the most mysterious number?

We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14.