Factorization Definition and 162 Threads

While I know the time complexity for all known prime factorization algorithms is exponential, I can't seem to get this results for a very simple algorithm. First assume we're doing this with numbers that are simply the product of two primes (the kind you get when working with RSA and others)...

I need to determine whether or not \mathcal{O}_{-10} = \mathbb{Z}[\sqrt{-10}] is a unique factorization domain. Now, I think the short answer is simply: NO. The question is meant to be simple (I think). I just finished proving that \mathcal{O}_{-5} = \mathbb{Z}[\sqrt{-5}] is NOT a...

Hello, I have got one mathematical problem and i am not able to solve it may i plese get some help. My sum is as foolws:- a^2+b^2=25 and a^3+b^3=91 so now find the values of a and b. Now here we cannot tahe into consideration that as a^2+b^2=25 , a=3 and b=4 or a=4 and b=3 .But we...

Find the LDL^T factorization of this matrix \left(\begin{array}{ccc}{2&-1&0\\-1&2&-1\\0&-1&2\end{array}\right) now i can find the L matrix by gaussian elimination that yields L = \left(\begin{array}{ccc}{1&0&0\\\frac{-2}{3}&1&0\\0&\frac{-1}{2}&1\end{array}\right) D =...

Franke et al. factored RSA640 using GNFS RSA640 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609 The Factors are...

Hi! How do I determine the number of distinct factors of a number, say, 2520? 2520 = 2*2*2*3*3*5*7 So we've 8 different primes. The number of combinations of those is, according to me: C(8,1)+C(8,2)+...+C(8,8)=155 (I think, calculated it by hand; but it isn't important) Obviously those...

I know how to solve quadratics using both factorisation and the equation method ... but how can i solve : (x-1)(2x-1)(3x-1) = 0 I multiplied it all out and i got .. 6x^3 - 2x^2 -3x -1=0 I just do not know where to got from here .. a little nudge in the right direction would be...

Is there a method one can use to obtain the prime factorization of a certain number? For example: Find the prime factorization of 49 + 39. [MathFest 2004] I realize that I can re-write the expression as 29.29+39, but that's about as far as I can go. :cry:

r^2 - xyr + (r^2)s + (x)r^2 - (y)r^2 + rsy Which terms should be grouped together for factorization? Please give some comments.

Would someone PLEASE help me. This is very basic, so I know this will be simple to you guys. I need to know how to break a random composite number down into its simplest prime form. Like 4=2 squared. Or like 12=3*2. I need to know how to make up larger composite numbers out of their most...

I have to prove that if ab is divisible by the prime p, and a is not divisible by p, then b is divisible by p. In order to prove this, I have to show (a,p)=1. I am not sure what this statement means. Then I am supposed to use the fact that 1=sa + tp when s,t are elements of the set of...

question : if p is a common factor of the equations f(x)=0, and g(x)=0, prove that p is also a root of the equation af(x) + bg(x) where a and b are constants. i want to know the working. i don't think the working will be like this : af(p) + bg(p) = a(0) + b(0) = 0 so, i need the...