Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20130428 12:48:26
Number Theory Problems1.For how many odd positive integers n<1000 does the number of positive divisors of n divide n? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20130428 13:24:16
Re: Number Theory ProblemsHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20130428 13:57:18
Re: Number Theory ProblemsNow, how can you say that those number's divisors have to be odd? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #4 20130428 14:09:25
Re: Number Theory ProblemsI am not sure what you are exactly asking so I will answer every possible question.
Odd numbers have odd divisors. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20130428 17:13:35
Re: Number Theory Problems
I'm not following this thread at all. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20130428 19:01:34
Re: Number Theory ProblemsHi Bob; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20130428 19:27:42
Re: Number Theory ProblemsAnd why not 9 as bob told? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #8 20130428 19:29:32
Re: Number Theory Problems
3^2 = 9 In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20130428 19:39:39
Re: Number Theory ProblemsOoh, do we search them manually? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #10 20130428 19:48:35
Re: Number Theory ProblemsThat is how I did it. You just square 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31 and check. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11 20130429 04:00:37
Re: Number Theory Problems
As bobbym pointed out, n must be a perfect square. n=1 is one possibility. For the others, it can be easily checked that all odd perfect squares greater than 1 and less than 1000 are have at most two distinct prime factors in their factorization. Thus the possibilities for n>1 are: where p and q are distinct primes and a, b positive integers. First case: The number of positive divisors of n are – i.e. there are positive divisors. So the possibilites are and . (Not ; that would make n too large.) Second case: There are only two such possible, namely and . The number of positive divisors for each number is 9, which does divide each number. Therefore the answer to your question is: There are 5 odd numbers less than 1000 which are divisible by their number of positive divisors, namely 1, 9, 225, 441, and 625. Last edited by Nehushtan (20130429 04:00:57) 134 books currently added on Goodreads #12 20130517 20:39:02
Re: Number Theory ProblemsWhat is the largest prime factor of 5^8 + 2^2? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #14 20130517 21:33:20
Re: Number Theory ProblemsHow did you come into that formula? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #15 20130517 21:44:30
Re: Number Theory ProblemsThere are things called aurifeuillian factorizations. This one could be the basis for many others. But like Aurifeuille who used it for n = 14 in 1871 there is much trial and error. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #16 20130517 22:10:08
Re: Number Theory ProblemsIsn't it just the a^2  b^2 formula? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #18 20130518 03:24:49
Re: Number Theory ProblemsOh Good one! Thanks!
By trying all of 2,3,5,7,11,13,17,19, and 23? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda 