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You are not logged in. #1 20120703 04:26:37
Deduce whether or not 4^545 + 545^4 is PrimeI am stuck on this problem. I've got it into this form: #2 20120703 04:29:58
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi zetafunc.; 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 20120703 04:32:20
Re: Deduce whether or not 4^545 + 545^4 is PrimeOh wow, I am such an idiot. It is a product, of course it cannot be prime. #4 20120703 04:36:22
Re: Deduce whether or not 4^545 + 545^4 is PrimeNot unless one factor is a 1 and the other the number itself. 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 20120703 04:40:34
Re: Deduce whether or not 4^545 + 545^4 is PrimeThe person who set the problem gave it being divisible by 73 as a hint, but I didn't know those were all the other factors. You used a computer to get those, right? #6 20120703 04:43:59
Re: Deduce whether or not 4^545 + 545^4 is PrimeI use cyclotomic polynomials which were first used by Lucas. 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 20120703 04:44:20
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi zetafunc. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20120703 04:47:41
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi; 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 20120703 04:53:43
Re: Deduce whether or not 4^545 + 545^4 is PrimeThey seem too complicated to use when we have a simple identity we know will solve our problem. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20120703 04:57:24
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi; 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 20120703 05:00:27
Re: Deduce whether or not 4^545 + 545^4 is Prime
Is there any chance you could explain how you can generate these? Sorry, I've never come across cyclotomic polynomials before, and I don't understand the Wolfram article... #12 20120703 05:04:18
Re: Deduce whether or not 4^545 + 545^4 is PrimeI just read the Wikipedia article.It might be clearer to read,zf. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #13 20120703 05:06:38
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi zetafunc.; 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. #14 20120703 05:07:57
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi anonimnystefy; 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 20120703 05:17:39
Re: Deduce whether or not 4^545 + 545^4 is PrimeThe very first line (1), what does the apostrophe/comma on top of the product symbol mean? Is that an error or does it mean something different? #16 20120703 05:20:44
Re: Deduce whether or not 4^545 + 545^4 is PrimeNever mind, I understand it now! Was just confused what to do for the value of n in my roots of unity, then just realised you're using it in (1). #17 20120703 05:21:21
Re: Deduce whether or not 4^545 + 545^4 is PrimeWhat did you develop the software in? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #18 20120703 05:22:59
Re: Deduce whether or not 4^545 + 545^4 is PrimeLooks like the absence of the comma is indicating that it's not restricted to the primitive roots of unity. Not sure how they differ to ordinary roots of unity, so will check the other article out. #19 20120703 05:41:18
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi anonimnystefy; 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. #20 20120703 05:41:59
Re: Deduce whether or not 4^545 + 545^4 is PrimeI am able to generate them, but I'm not sure how I can use them here? #21 20120703 05:46:32
Re: Deduce whether or not 4^545 + 545^4 is PrimeMe neither but you try to get yours into one of the forms. 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. #22 20120703 05:53:12
Re: Deduce whether or not 4^545 + 545^4 is PrimeBut how is the Sophie Germain identity generated from cyclotomic polynomials? I can sort of see where you are getting your x^18  1 from (the factors are all cyclotomic polynomials) but how do I then get that into a useful form, such as your a^6 + 8b^6 example? #23 20120703 05:54:46
Re: Deduce whether or not 4^545 + 545^4 is PrimeHi; 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. #24 20120703 05:57:59
Re: Deduce whether or not 4^545 + 545^4 is PrimeI read the Wolfram article again and looked at (21), (22) and (23), I can see where you got the factors from now. So cyclotomic polynomials cannot be used for this particular problem because of the two variables? #25 20120703 06:34:57
Re: Deduce whether or not 4^545 + 545^4 is PrimeThere is a general method for all types of problems like this one. 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. 