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Random Math Thread : Puzzles , Jokes , Problems, Funny Anecdotes, Random Thoughts


Science Friction

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I love mathematics and I'm hoping there are a few others who enjoy it as well. Feel free to post any thoughts about the subject in this thread. Maybe there's a calculus problem that you would like someone to solve or maybe you have a puzzle, a riddle, a mathematical paradox, or just something interesting or funny that you came across that is math-related. Maybe you just want to interject some random thoughts about math or how you or someone you know has used or misused it. Whatever your thoughts, I'd enjoy hearing them.

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I'll leave you with this to ponder for today. You have heard of prime numbers, of course(2,3,5,7,11,13,17,...). But what about PERFECT numbers? A perfect number is a number which is equal to the sum of its proper divisors. EX: 6 is a perfect number since 6 = 1+2+3 . Can you come up with the next one?

 

Interestingly enough, there is a relationship between primes and perfect numbers, which I will give in the next post. You should be able to easily find the perfect number that follows 6. But what about the third one? It's quite a bit larger(three digits). If you have trouble determining it, the next post should help you generate as many of them as you want.

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If (2^k) - 1 is prime ,where k is a positive integer , then [ 2^(k-1)][ (2^k)-1] is perfect.

 

Example: for k = 2 , we have (2^k)-1 = 3 (prime) . Thus, [ 2^(2-1)] [(2^2)-1] = 2*3= 6. So, k = 2 yields the perfect number 6.

 

Try k= 3 to generate the next perfect number.

k= 5 will generate the one after that.

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If (2^k) - 1 is prime ,where k is a positive integer , then [ 2^(k-1)][ (2^k)-1] is perfect.

 

Example: for k = 2 , we have (2^k)-1 = 3 (prime) . Thus, [ 2^(2-1)] [(2^2)-1] = 2*3= 6. So, k = 2 yields the perfect number 6.

 

Try k= 3 to generate the next perfect number.

k= 5 will generate the one after that.

 

This is like trying to read Chinese.

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