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Sep
26
comment How many ways can I make six moves on a Rubik's cube?
@Henry: You are right. actually the number I gave allows 18 legal moves while the OP ask for 12 (90 deg twists) so the number of different positions after at most 6 moves is a lot smaller: 1056772. Actually the method given by him (make six random moves until the puzzle is solved) fails for the 96696 positions after 5 moves if it does not take this into account.
Sep
24
comment The number of ones in a binary representation of an integer
@Matt: Why 16x increase? I'm not sure I agree, as you are substituing a few cheap operations with table lookup which needs slow memory access and messes the cache.
Sep
24
answered The number of ones in a binary representation of an integer
Sep
12
comment Bound for divisor function
$\mathrm{Li} x$ is the logarithmic integral $=\int_2^x \frac{ dt}{\log t}$ see here.
Sep
12
answered Bound for divisor function
Jun
21
answered Calculating monodromy
Jun
20
revised Finding the integer $\le n$ with largest number of divisors
added 11 characters in body
Jun
19
awarded  Student
Jun
19
asked Finding the integer $\le n$ with largest number of divisors
May
5
comment Example of a rational function such that : $(f(x))^{3} + (g(x))^{3} + (h(x))^{3}=x$
@lhf: In the page linked by Gerry you have several solutions and links as: $(m^3-3^6n^9)^3 + (-m^3+3^5mn^6+3^6n^9)^3 + (3^3m^2n^3+3^5mn^6)^3$ $= m(3^2m^2n^2 +3^4mn^5+3^6n^8)^3$.
Mar
19
answered Common terms in general Fibonacci sequences
Mar
13
revised The number of symmetric polynomials of n degree
Error Corrected
Mar
13
revised The number of symmetric polynomials of n degree
added 828 characters in body
Mar
13
awarded  Commentator
Mar
13
comment The number of symmetric polynomials of n degree
I don't understand what you mean by invariant, do you mean homogenous?, all the terms have the same total degree? take this four examples with $n=3$ and $k=2$, a) $x^3+y^3$, b) $x^2y + xy^2$, c) $x^3+y^3 + x + y$ d) $x^2y + xy^2+x+y$, which are you counting as degree 3?
Mar
13
answered The number of symmetric polynomials of n degree
Mar
11
comment Find maximum divisors of a number in range
PARI-GP is a great program to perform number theoretic calculations. The algorithm I've used is the same I have described, but PARI-GP knows how to handle big numbers and that makes everything easier.
Mar
11
revised Find maximum divisors of a number in range
added 317 characters in body; added 2 characters in body
Mar
11
answered Find maximum divisors of a number in range
Mar
8
comment Help complete a proof of Dirichlet on biquadratic character of 2?
2 is a biquadratic residue if and only if there is an $y$ with $y^4\equiv 2\pmod{p}$ if and only if $2^{(p-1)/4} \equiv (y^4)^{(p-1)/4} \equiv 1 \pmod{p}$ the last iif can be seen for example using a primitive root mod $p$.