... That was 9 months ago. Since then, this "learning process" by David, Kevin and me has continued, and if you visit that link you will find that those 18...
... if p= 4*k +1, and q= 2*p +3 are both prime, then if [(Mp)^p -p] mod q== N, and q mod N== +/-1, then (Mp), the base... is prime. (someone would have to...
clarification: also, if (Mp) mod p = 1 and N = 0, then if N = 0, then that (Mp) is prime as well. ... {typo correction} = -2 -1 and (-3)^5 -5 = -248 and...
either if (Mp) mod p = 1, and N is a square, then (Mp) is prime as well, or simply iff (Mp) mod p == 1, then choose a different 'p'. I believe it works now. ...
Please repeat in full corrected state or give us notice of where in print that is to be found at some time. I cannot read the combination and this looks...
so many times, there are typos when using e-mail. in math, Mp is often used to describe a Mersenne number with a prime expo- nent. I have corrected it to (Mr)....
For r=6, Mr is composite but p=5, q=13, N=2 yields a counter-example. What about r=37, p=23593, N=1 ? all your conditions are satisfied, but Mr is not prime. ...
I agree. it will be difficult to formalize the conditions without knowing how to construct the Lagrangian-style proof. it wouldn't be when r is not prime, and...
How many ways can the square of an odd prime n be expressed as the sum of four non zero squares? The answer surprisingly appears to have the formula: f =...
How do you write 5 as sum of four nonzero squares ? Maximilian PS: if you haven't heard back from OEIS, the messages may have been sent to trash by your spam...
I'm sorry, I did not read the definition correctly, I missed "the square of" the odd prime. I checked and found it indeed surprising that neither of the...
I just looked, and yes indeed it went to a spam folder. But it was sent just today, five hours ago. I looks like I will have to do some editting to make it...
the 4 equations for a Mersenne number (Mr) where r is prime. (either one or the other is true) p=4k+1, q=2p+3 (both prime) [(Mr)^p-p] mod q == -1, or p=4k+3,...
Hello group, What is the next term of the following serie a(n): a(1) = 2 a(2) = 2 a(3) = 2 a(4) = 296 a(5) = 369719 a(6) = 457578 a(7) = ? Opened question: is...
... Thank you David. A friend told me that your code demonstrates that your g(x) function appears to have my sequence as coefficients. I must confess I am...
Actually David gave simply the g.f. (generating function) of the sequence f(n)=floor((n^2+4*n+24)/48) In some sense there is no "higher" number theory involved...
... Thanks, that was the goal. I thought I might point out this article refers to our list of references about the primality of one with a "URL to be...
... Indeed. It seemed to me that g(x) = x^4/((1-x)*(1-x^3)*(1-x^8)) = suminf(n=0,f(n)*x^n) made Mark's conjecture ... look neater. I made no attempt to prove...
... Well, the maths is so far above my head I cannot comment on it at all. However, I must say that I'm worried that he seems to be working in a vacuum - about...
... Hum, "In this case, in which r=2, sqp(abc)^r/c is nearly always greater than 1, and always greater than zero. " "Nearly always" does not mean anything, and...
... Actually the ABC conjecture states that for any r > 1, sqp(abc)^r/c > 1, except for some finite number of exceptions. There's your "nearly always",...
Phil Carmody has suggested that there are standard texts that are not pertinent in reference. Â Phil, would you be so kind as to name these (to facilitate...
... The claimed inequality of "bounded discrepancy classes" in Theorem A of Paper IV is mind-boggling general; much wider than ABC. It may take a long time for...
