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1. Simple probability distribution function on gnuplot

Hi, I am trying to plot a graph I have made using excel on gnuplot. I have converted the excel book to a csv file and the data I have looks like this 0,0.166341305 1,0.000000159 2,0.000000159 3,0.000000159 4,0.000000159 5,0.000000159 ... and so on for 2048 different points. The data...
2. Factoring large N into prime factors

thanks, that's perfect. The way in which i found (p-1)(q-1) is to take a set of sequences of powers of x mod N for x=1,2,...,N-1 and work out their periods, each period turns out to be a divisor of (p-1)(q-1), if a large enough number of divisors is taken, then the value of (p-1)(q-1) can be...
3. Factoring large N into prime factors

Hi, I am writing up a project based on an algorithm for factoring large numbers, I have reached seemingly simple point where I am stuck, I wonder if anyone can help me? I am trying to factor a large N such that N=pq for unknown primes p and q, I have described a method to find a value for...
4. Infinitary union combined with infinitary intersection

this helped a lot, thank you
5. Infinitary union combined with infinitary intersection

I am struggling with combining infinite unions with infinite intersections, the problem i have is to show that, for Sets Aij where i,j \inN (N=Natural Numbers) ∞....∞ \bigcup ( \bigcap Aij) i=0 j=0 is equal to .....∞ \bigcap{(\bigcupAih(i):h\inNN}...