What is Adam Number?

An Adam number is a positive integer such that when you square the number and also square its reverse, the reverse of the square of the number is equal to the square of the reverse. In simpler terms, a number whose square and the square of its reverse are reverses of each other.

Definition and Explanation

An Adam number possesses a unique property related to its square and the square of its reverse. Here's a breakdown:

1. Reverse the Number: Take the original number and reverse its digits.
2. Square Both: Calculate the square of the original number and the square of its reversed counterpart.
3. Check for Reversibility: Determine if the square of the original number is the reverse of the square of the reversed number. If it is, the original number is an Adam number.

Example

Let's examine the number 12 to see if it qualifies as an Adam number:

1. Original Number: 12
2. Reversed Number: 21
3. Square of Original: 12² = 144
4. Square of Reversed: 21² = 441
5. Check: Is 144 the reverse of 441? Yes!

Therefore, 12 is an Adam number.

More Examples

Here's a small table listing some Adam numbers:

Number	Square	Reversed Number	Square of Reversed Number
12	144	21	441
13	169	31	961
22	484	22	484
31	961	13	169
102	10404	201	40401
112	12544	211	44521

Key Characteristics

• Adam numbers are positive integers.
• The reversing process involves treating the number as an integer, not a string.
• The squares must be perfect squares of both the original and reversed numbers.

Importance

While Adam numbers don't have direct applications in major fields like cryptography or engineering, they represent an interesting mathematical curiosity and contribute to the exploration of number patterns.

In summary, an Adam number is a number whose square and the square of its reverse are the reverse of each other.