Recent content by rscosa

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    Zeta function in the critical strip

    Hi!, there are many other representations (wikipedia or but maybe non of them will be enough helpfull.
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    Riemann Zeta zeros

    Hi!, there is NOT an official proof but many people is trying hard.
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    Fermat's Last Theorem, proof by Andrew Wiles

    Hi! if you are undergraduate or even if you are PhD (as I am) and you read those paper you can become crazy, if you do not then for sure you need a big bottle of aspirines :). By the way I read them and I am alive and not enough crazy!
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    Carmichael number

    Hi! I suggest you to read more before publish your problems since this is a very well known question (Wikipedia).
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    Unsolvable exponental?

    Hi! it is impossible to find a explicit expression for the solutions of you equation because that means that you can solve the integral x^x which is impossible to express in tems of elementary functions (read wikipedia about this topic) so the answer is: You only can get numerical approximation...
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    Prime Numbers

    Hi! Something like: L_n=L_{n-2}+L_{n-3} with L_0=0, L_1=2, L_3=3 also called the Perrin sequence.
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    Pi in binary

    Hi! the answer to this question, IMPOSSIBLE, because you dont have the whole number in memory but just an approximation of PI, so you can get a very acurate approximation of the approximation of PI :).
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    Identity of Zeta function

    Hi, I think the problem is not well-defined, the first part is a functional and the second a function. Please, be more especific. But I guess there is some relation like this.
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    X^2+y^2+z^2=nxyz n is natural

    Hi, The answer is described ad a hyper-surface of dimension 2 except if you are talking about a diophantic equation over the integers, please be more especific.
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    Imaginary Zeros of Zeta Function

    Hi! The Riemann Hypothesis clames that if RZF(z)=0 and z is not a trivial zero, then Re(z)=1/2. That is all. The real part of z needs to be equal to 1/2 (there is NOT restriccion about the imaginary part of z). And 0=0+0 I=ZERO. RFZ= Riemann Zeta function.
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    Mobius Inversion, finite subgroup

    Hi! I can not help you with the part of $\psi$ function but yes with the other part. It is well known that x^{n}-1=\prod_{d|n}\Phi_d(x), where \Phi_d is the dth-ciclotomic polynomial which has degree \phi(d), in other words, the euler function of d, so know (a) should be striagtforward...
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    Chance of random walk returning to origin

    Hi! the answer of this problem is not known yet. I know the answer if you are in a line at some point and you wanna know the probability to return to 0 which can be written in terms of the hyperbolic sine by using really complicated mathematics (not for undergraduates).
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    Where Fibonacci numbers surpass prime numbers

    Hi! I think your conjecture is wrong although to find a counterexample you need to go so so far away. The Fibonacci sequence satisfies the recurrence relation: $F_n=F_{n-1}+F_{n-2}$ with $F_1=1$ (or $0$ depends how you define it but it does not matter). Now, if you consider the recurrence...
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    Riemann Zeta zeros

    Hi! fortunately all the complex zeros outside of the known strip are negative and even integers, so of course all of them are (complex but real) zeros of the RZF and have the same imaginary part (equal to zero). But the RZF has no zeros with nonzero imaginary part outside of the strip $0<\re...