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

You are not logged in. #1 20130813 02:13:53
Integer Relation?!How do you solve something like: 3a + 4.2b + 7c + 10.5d = 59.3 over the integers? '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 20130813 02:17:52
Re: Integer Relation?!Hi; 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 20130815 01:27:00
Re: Integer Relation?!Yes! They wanted positive int solutions. '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 20130815 01:32:22
Re: Integer Relation?!Yes a PSLQ can do that and is the method of choice. Then you use generating functions to prove it is the only solution. 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 20130815 02:08:11
Re: Integer Relation?!I do not know if it is classical mathematics or not but let us keep the debate for later. '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 #6 20130815 02:10:11
Re: Integer Relation?!Hmmm, how do you define by hand? Where is the problem from? 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 20130815 02:25:25
Re: Integer Relation?!brilliant. '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 20130815 02:35:21
Re: Integer Relation?!So, you have put me back into the 19th century. First of all, I want to tell you I do not like that century. Have I ever told you the story of how grandpappym killed 30 Union soldiers with just his revolver a bayonet and his hands? It was September of 1863 ( the nineteenth century ) at the battle of Chickamagua, but wait I am getting off the point. 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 20130815 03:16:08
Re: Integer Relation?!Empirically? ?? '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 20130815 03:26:56
Re: Integer Relation?!The other three numbers are all divisible by 5. So some multiple of 593  42 b must also be divisible by 5. Only 2 numbers 4 and 9 for b do that. 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 20130815 03:33:23
Re: Integer Relation?!Why not anything greater than that? and only that? '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 #12 20130815 03:39:40
Re: Integer Relation?!{551,509,467,425,383,341,299,257,215,173,131,89,47,5,37} 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. #13 20130815 03:46:19
Re: Integer Relation?!hmm... '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 20130815 03:56:42
Re: Integer Relation?!Easy to see that 215 can not be the sum of 30,70 and 105 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. #15 20130815 04:14:40
Re: Integer Relation?!
I could do that, but the rest were tough. '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 #16 20130815 04:18:35
Re: Integer Relation?!What part? 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. #17 20130815 11:58:24
Re: Integer Relation?!How do you write a PSLQ? '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 20130815 12:00:10
Re: Integer Relation?!I think anonimnystefy and I were discussing that same problem. I do not even remember what the answer was. 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. #19 20130815 12:07:13
Re: Integer Relation?!But you certainly remember the algorithm '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 #20 20130815 12:10:49
Re: Integer Relation?!The algorithm is written in M. It uses a built in command called Lattice Reduce. That is what I can not do. 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. #21 20130815 21:09:42
Re: Integer Relation?!Why did you link me to page 11? '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 #22 20130815 23:01:38
Re: Integer Relation?!It is a whole discussion of Lattice Reduction. 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. #23 20130816 01:31:18
Re: Integer Relation?!I can understand it but I don't think I will be able to do the same for any other problem '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 #24 20130816 02:14:41
Re: Integer Relation?!That method like all book methods is only possible for a few types of problems. I could easily change the problem to be intractable. 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. 