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Apr
14
awarded  Popular Question
Jul
2
awarded  Curious
Apr
5
comment Missing one link in logic of basic unique factorization argument
Wait, that's not right. Only that when in lowest terms the equality holds. And then each side can be multiplied (denominator and numerator) by whatever one likes. And the equality still holds since that is the same as multiplying by 1. Phew. I think that settles it.
Apr
5
accepted Missing one link in logic of basic unique factorization argument
Apr
5
comment Missing one link in logic of basic unique factorization argument
Okay, if we say that the GCD of the GCD of both denominators and the GCD of both numerators is not 1, I think that settles it. So something can be cancelled from one side, or both sides. So P has a multiple in common with R, and A has a multiple in common with K and these two common multiples have a common multiple, that is not 1, then at least one side is not in lowest terms. Is that right? That sounds more right. I thought it still felt funny. Thanks for pursuing and pointing that out.
Apr
5
comment Missing one link in logic of basic unique factorization argument
I suppose there would be not factor common between numerator and denominator. So if there is then it can't be in lowest terms. Okay, thanks for repairing my logical chain, I think I'm convinced. :)
Apr
5
comment Missing one link in logic of basic unique factorization argument
Oh, since P must be a multiple of R and A must be a multiple of K, because of the equality?
Apr
5
asked Missing one link in logic of basic unique factorization argument
Mar
25
comment Deligne and the four Weil statements about polynomials over finite fields?
@GregMartin that's a good distinction I never thought of making clear before.
Mar
24
comment Deligne and the four Weil statements about polynomials over finite fields?
@Martin Okay, thanks. That pdf looks to be pitched at the right level. At a cursory first inspection. Thanks again.
Mar
24
revised Deligne and the four Weil statements about polynomials over finite fields?
added 35 characters in body
Mar
24
comment Deligne and the four Weil statements about polynomials over finite fields?
@GregMartin Solve polynomials over finite fields . . . Obtain values, in some finite field, of the variables of that polynomial, whose coefficients in same finite field, such that the polynomial evaluates to zero. 1 set of such variables is a 'solve' or a solution. The find the number of these is to count the solutions. I believe that Deligne's work had something to do with counting the number of solves.
Mar
24
asked Deligne and the four Weil statements about polynomials over finite fields?
Mar
22
comment A weird question on measuring the randomness of a sequence of integers via expected behavior of gcd
Okay so we have a possible measure for randomness by sampling the GCDs and seeing if the occurrence of co-primality reproduces the distribution $1/\zeta(i)$, for i samples. This is good. Geometric progression will always have a GCD with probability 1. Arithmetic I am unsure of. Prime gaps will have pairwise GCD = 2 with probability 1 in the limit, and then GCD = 4, 6, ... with some discoverable distribution. The compressed bytes will likely obey the above 'random' metric, and the text of Naruda is a case that would have to be closely examined in the ring mod 257.
Mar
22
asked Weierstrass factorization of sine, and related questions
Mar
22
comment A weird question on measuring the randomness of a sequence of integers via expected behavior of gcd
Nice result. The probability that any two selected integers will have a factor n? for sum(1/n*1/n) for all n? sum of reciprocal of squares right.
Mar
22
revised A weird question on measuring the randomness of a sequence of integers via expected behavior of gcd
added 179 characters in body
Mar
22
comment A weird question on measuring the randomness of a sequence of integers via expected behavior of gcd
@Did haha. Good point. Okay, I was hoping that sentence would avoid having to explain what random is. You found me out.
Mar
15
accepted Simple resource for Lagrangian constrained optimization?
Mar
15
asked Simple resource for Lagrangian constrained optimization?