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Happy Numbers are Part of Recreational Math Essay

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Happy numbers are a part of recreational maths. I will also talk about happy cube numbers, they are the same as happy numbers, but instead of squaring the digits of the original number, the digits are cubed. Furthermore, I will also explore happy prime numbers, these are prime numbers which are also happy. Additionally, I will mention unhappy numbers, these are numbers that do not end in 1 instead they loop in a cycle around number 4. Lastly, I will explore the history and real life uses of happy numbers, such as in computer programming and encryptions.

History of happy numbers The origins of happy numbers is not clear, the first time they were mentioned was during the 20th century. Likely guesses are that they originated from
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1+6=7, 7 is a happy number. All numbers that are 10ˣ are also happy numbers, this is because their digits will always be one 1 and one or more 0’s. an example would be 10²=100 and 100 is a happy number. Furthermore if a happy number N has one more zero added to the end of it, it will still be a happy number this is because zero does not affect the sum of the squares. An example is 13 is a happy number and so is 130. 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…..

Unhappy numbers Unhappy numbers are numbers that after having their digits squared and added together repeatedly the number always leads to 4. This is how you find out if a number is unhappy:
16:
1²+6²= 1+36= 37
3²+7²= 9+49= 58
5²+8²= 25+64= 89
8²+9²= 64+81= 145
1²+4²+5²= 1+16+25= 42
4²+2²= 16+4= 20
2²+0²= 4+0= 4 As you can see, 16 is an unhappy number. This sequence is a continuous cycle because 4²=16, and the whole thing will start all over again. 37, 58, 89, 145, 42, 20, and 4 are also all unhappy numbers because they are all part of the sequence. This means all these numbers also loop around the number 4 in a cycle.

Happy Cube Numbers Happy cube numbers are numbers that when their digits are cubed and added together repeatedly they will equal to 1. They are the same as happy numbers except that their digits are cubed instead of squared.
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