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2d
awarded  Revival
2d
revised Is it true that for infinitely many values of $n$, the sum of digits of $2^n$ is greater than for $2^{n+1}$?
minor typographical edits
2d
answered Is it true that for infinitely many values of $n$, the sum of digits of $2^n$ is greater than for $2^{n+1}$?
Jul
24
awarded  Nice Answer
Jul
23
answered Prove that if the sum of each row of A equals s, then s is an eigenvalue of A.
Jul
19
comment Congruence of nth degree
Please help by explaining your own thoughts first.
Jul
19
comment Congruence and percentage
@Doop The percentage conditions reduce $x,y,z$ to a 1-dimensional lattice: $(x,y,z)$ must be an integer multiple of some tuple $(x_0,y_0,z_0)$ where $x_0,y_0,z_0$ have no common factor (this is essentially $(\alpha,\beta,\gamma)$ divided by the gcd). Say that multiple is $t$, then each of the modular constraints on $x,y,z$ can be reduced to a modular constraint on $t$ (possibly with a smaller modulus). Then reconcile all three constraints by Chinese remaindering.
Jul
18
comment Congruence and percentage
@MattB. Note that the last three equations are not linearly independent (or rather, if they are then it forces $x=y=z=0$), so this isn't really 6 equations in 6 unknowns. I'd imagine a generic instance would have $\alpha + \beta + \gamma = 1$, much like the one given by Doop in the comments.
Jul
17
comment Sum of reciprocals of primes for known primes.
@fretty Given that the sum is feasible to compute, doesn't this answer your latter question affirmatively?
Jul
13
revised Sum of reciprocals of primes for known primes.
added 408 characters in body
Jul
13
answered Sum of reciprocals of primes for known primes.
Jul
10
answered Proof completion: Determine a simple expression for $\tau(G)$ in terms of the vertex degrees of $G$. (details inside)
Jul
9
comment Prove $a^m\equiv a^{m-\phi(m)}\pmod m$ for all positive integers
You mean $m=yk$ in the definition of $y$, right? This probably boils down to proving that $m-\phi(m)$ is large enough compared to the highest exponent of any prime power dividing $m$ (which is bounded by $\log_2(m)$, for starters).
Jun
30
comment Infinitely many prime $n$ for which $n^2 = p + 8$ for some prime $p$.
@anorton I believe even the weaker statement "there exists a quadratic univariate polynomial taking on infinitely many prime values" has not been proven. The closest we have to this are Sierpinski's theorem that there exist polynomials of type $n^2+r$ which take on arbitrarily many prime values, and Iwaniec's theorem that $n^2+1$ is prime or almost-prime infinitely often (this has been extended to all quadratics which satisfy Bunyakovsky-type constraints).
Jun
21
comment How solve this question
@Seeker Really? But didn't you write "I have no clue what to begin with, a hint would suffice"?
Jun
20
comment How can I show that $\phi(m) \mid \phi(n)$?
Shouldn't the first product subscript be $p \mid n$? This is a rather unconvincing argument, as $\phi(n)$ includes more fractional factors than $\phi(m)$ in the above representation.
Jun
16
comment Taylor series $\ln(2+x)$ centered at $x=2$
The series you give has infinite radius of convergence, so it can't possibly represent $\ln(2+x)$.
Jun
8
comment What is the definition of 'within one' in mathematics
I'd also add that the use of $\pm$ to mean "within" is less common in mathematics, where $\pm 1$ is generally used to mean "+1 or -1" and no possibilities in between (e.g. in the quadratic formula).
Jun
8
reviewed Close A question on particular functions in $L^\infty$
Jun
8
reviewed Close What is the next number in the integer sequence $3, 3, 4, 2, 1…$