In collaboration with Kalpok Guha, we made a set of problems based around the topic of "types of numbers". There are many types of numbers out there and here are just a few of them.
This set serves primarially to teach everyone about the complexity of numbers and the many interesting properties they have because math is . Except for trig.... Trig is not pretty (lol, I'm bad at trig).
Note: most of these problems are doable by hand using a NT approach but a CS approach works just as well.
The "special" numbers include:
Multiplicative perfect numbers- those whose factors when multiplied (including the number itself) yield .
Amicable pair- a number whose factors sum to and the factors of sum to .
Abundant number- a number whose factors including itself sum to greater than .
Deficient number- a number who's factors including itself sum to less than
Perfect number- a number who's factors including itself sum to
Narcissistic number- a number of digits that can be represented by the form and can be written in the form where is a whole number and for some positive integral value of .
Or I'm simplier form, a narcissistic number is one that when each individual digit is summed to the nth power, their sum is the original number.
I must say making this problem set taught me a lot of cool properties about numbers, some that I can't post because I can't think of a problem for them.
I even learned how to spell narcissistic: n-a-r-c-i-s-s-i-s-t-i-c,