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1h
comment difference between slopes of lines represented by an equation
An equation has an equals sign in it. You haven't given an equation.
1h
comment Is $\pi^k$ any closer to $[\pi^k]$ than expected?
$[x]$ is the notation for the largest integer not exceeding $x$, so $0\le x-[x]<1$. If you want the closest integer to $x$, find a different symbol for it. In any event, the question you are asking is a notorious unsolved problem in diophantine approximation. It's not even known whether the fractional part of $(3/2)^n$ is uniformly distributed.
1h
comment solve for variable in combination
Any thoughts on the answers that have been posted?
1h
comment $2^k+3$ : Primality Brute Forcing Theory Below The Square Root
OK, so you're asking whether $2^k+3$ always has a factor much much smaller than its square root, unless it's prime. Seems unlikely.
7h
comment Checking whether a given polynomial is reducible or irreducible.
But it seems OP has been asked to prove some polynomial (we can only guess which polynomial) is irreducible over the rationals but reducible over the reals. So we're probably not talking about $x^2+1$.
7h
comment Proof: For every positive integer $n$, there is a sequence of $n$ consecutive positive integers containing no primes.
It doesn't. But $(x+i)/(i+2)$ does.
7h
comment $2^k+3$ : Primality Brute Forcing Theory Below The Square Root
The number you have after Step 5 is bigger than $\sqrt{2^k+3}$, so of course if no number below that number divides $2^k+3$, then $2^k+3$ is prime. This would work with any starting number (Step 4 is superfluous).
7h
comment Checking whether a given polynomial is reducible or irreducible.
@QiaochuYuan, I hope OP is not being asked to prove $x^2+1$ is reducible over the reals. Maybe $x^2-2$ was meant.
7h
comment Math Rap fact check
But the torus doesn't have zero curvature, right?
1d
comment Counting integers from $1$ to $n$ with an odd number of divisors in {1,2,3,…,k}
The most efficient way may be to divide each number from 1 to $n$ by each number from 2 to $k$ and count how many have an odd number of divisors. Or, it might be to factor every number from 1 to $n$ and produce all the factors of each number from 1 to $n$ and then for each see how many of those factors are between 1 and $k$. Come on, give us some information. Why do you need an efficient way to solve this problem? What range of values of the pair $(n,k)$ do you envision? Is it just a one-off, or do you need to calculate millions of these? Don't keep secrets – help us help you.
1d
comment Convergence of improper integral $\int_{2}^{\infty} \frac{1}{log(t)}dt$
I note that this is a very important integral in Number Theory, as the integral out to $n$ is asymptotic to the number of primes up to $n$.
1d
comment What does a variable superscript above a set mean?
I think Carl meant, repeated Cartesian products.
1d
comment Show that any vertex $v$ of $P$ is half-integral.
@Carl, you wouldn't be notified if I used "Chris". And I don't get notified when you leave a space between the at-sign and the Gerry.
1d
comment how to find coefficient c1, c2, c3, c4 of a polynomials of degree 4 from resolvent
Are you still here?
1d
comment find a value in pascal triangle given row and column
I say, what seems tough about the Lucas formula?
1d
comment Finding $\sqrt{17}$ and $\sqrt{257}$ in the regular $17$-gon and $257$-gon?
For what it's worth, Tito, a line segment is just a difference of two roots of unity.
2d
comment Can an infinite sum of irrational numbers be rational?
This may fail the "linear combination" condition, although that condition needs explication.
2d
comment Is $\arctan2$ irrational?
It's known that the only rational values of $x$, $0\le x<1/2$, such that $\tan \pi x$ is rational are $x=0$ and $x=1/4$.
2d
comment Counting integers from $1$ to $n$ with an odd number of divisors in {1,2,3,…,k}
I doubt there's any useful exact formula for this function of two variables. What is it that you really need to know?
2d
comment Propositional-Calculus/ Set Theory Proof using Identities
I don't know what that means, but whatever it means, it should go in the body of your question, so people don't waste their time, and yours, with answers you don't want.