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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.
1h
comment A monotonically increasing series for $\pi^6-961$ to prove $\pi^3>31$
@Ewan, if that's what OP means, perhaps he will edit the body of the question in the light of your comment.
10h
comment Can an infinite sum of irrational numbers be rational?
This may fail the "linear combination" condition, although that condition needs explication.
10h
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 $x=1/4$.
10h
comment Counting integers from $1$ to $n$ with an odd number of divisors less than or equal to $k$
I doubt there's any useful exact formula for this function of two variables. What is it that you really need to know?
10h
comment A monotonically increasing series for $\pi^6-961$ to prove $\pi^3>31$
Of course there is a series for $\pi^6-961$ with unit fraction terms – every positive real number can be written as a sum of unit fractions. But maybe you meant to write something else?
16h
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.
16h
comment Propositional-Calculus/ Set Theory Proof using Identities
Truth tables?${}$
16h
revised How to calculate with complex arguments?
edited tags
16h
answered Finding $\sqrt{17}$ and $\sqrt{257}$ in the regular $17$-gon and $257$-gon?
1d
comment Finding homomorphisms in normal groups to $S_n$
OK, Jay. You might want to delete the question, then. Meanwhile, I'll vote to close it.
1d
comment find a value in pascal triangle given row and column
Your question asked how to find a value, but now it seems you want to find all the values. If you just want to find one binomial coefficient modulo $p$, it's hugely inefficient to first find the 10,000 values before the one you want. Also, what exactly seems tough about the Lucas formula?
1d
comment Four of a kind from a 3d pack of cards
@Thomas, you're right; one has to calculate those numbers as well, and then appeal to Inclusion-Exclusion.
1d
comment counting steps in Collatz Sequence
It is 8. Someone has made a mistake.
1d
comment Four of a kind from a 3d pack of cards
So, how many ways can you get 4 red cards? how many ways can you get four 3s? how many ways can you get four Bs? How many total deals are there? how should you put all these numbers together?
1d
comment $x^4 - y^4 = 2z^2$ intermediate step in proof
You may want to work out the possible values of $\gcd(x^2+y^2,x+y)$, $\gcd(x^2+y^2,x-y)$, $\gcd(x-y,x+y)$.
1d
comment Given a basis $U$, what conditions are needed for an orthogonal basis for it?
Good! Let me encourage you to write up what you now understand, and post it as an answer.
1d
comment Given a basis $U$, what conditions are needed for an orthogonal basis for it?
OK, now that you have edited it, the answer is, of course not. If you just take any old vector orthogonal to $(1,1,1)$, there's no reason to think you will get $(1,3,7)$ in the span, so no reason to think you will get $U$. Think geometrically! You have a plane, you have one vector in that plane, you take a second vector orthogonal to the first one, if that second vector is not in the plane, then the two vectors can't possibly be a basis for the plane!
1d
comment Given a basis $U$, what conditions are needed for an orthogonal basis for it?
Given any subspace of ${\bf R}^n$, there is an orthogonal basis for that subspace. Given any basis for a subspace of ${\bf R}^n$, you can use GS to construct an orthogonal basis for that subspace. Every basis is fine, but the orthogonal ones are finer. Your question is exceedingly unclear. What do you really mean?
1d
comment find a value in pascal triangle given row and column
Good! But, 1) you still need to calculate $A$ and $B$, each a product of as many as $10^5$ numbers, 2) Fermat's Little Theorem, as a way of finding an inverse modulo $p$, is vastly inferior to the (Extended) Euclidean Algorithm), and 3) DID YOU LOOK AT THE LINK TO LUCAS' THEOREM?