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May
16
revised Integral estimate
deleted 1 character in body
May
13
comment Prove the sequences $\lfloor \alpha n\rfloor $ and $\lfloor \beta n\rfloor $ are disjoint
@GabrielR. How many of the numbers in the first sequence are smaller than $n$?
May
13
comment Prove the sequences $\lfloor \alpha n\rfloor $ and $\lfloor \beta n\rfloor $ are disjoint
@i707107 Do you think that this is a good hint?
May
13
comment Existence of functions which satisfy some conditions
For you, too: spikedmath.com/170.html
May
13
comment Existence of functions which satisfy some conditions
spikedmath.com/170.html
May
13
comment Prove the sequences $\lfloor \alpha n\rfloor $ and $\lfloor \beta n\rfloor $ are disjoint
Try to count how many numbers in both sequences together are of size at most $n$.
May
12
comment How do we pronounce this symbol?
@Mathias711 It used to be one of the community ads, I do not know if it is now.
May
12
comment How do we pronounce this symbol?
Detexify can sometimes help with this kind of question: detexify.kirelabs.org/classify.html
May
11
answered Prove that the following limit exists and find it!
May
11
revised Inscribed Angles in Two Cyclic Quadrilaterals
edited tags
May
11
answered Inscribed Angles in Two Cyclic Quadrilaterals
May
11
comment Inverse Identity + Constant Matrix
However, I would be quite impressed if someone found this without ever having seen something similar.
May
11
comment Inverse Identity + Constant Matrix
@AimForClarity First of all, I have seen the matrix with only 1s in other problems before, so its properties are already at the back of my head. In general, you can express any inverse matrix as polynomial in the matrix (just multiply the minimal polynomial by the inverse), so I am already motivated to look at this. To find the minimal polynomial directly, it is clearly useful to calculate $B^2$ and the identity $B^2=nB$ tells me that the minimal polynomial for $I+B$ must have degree 2, so the expression for the inverse (if it exists) must have degree 1 in $B$.
May
11
comment Generalization of Binomial Coefficients Congruence
@sm654567 I am not sure what you mean. What you want is usually the key lemma in any proof of Lucas theorem and it only uses elementary facts, the binomial theorem and the fact that $p$ does not divide factorials of smaller numbers.
May
10
answered Generalization of Binomial Coefficients Congruence
May
7
comment Inverse Identity + Constant Matrix
That is correct (if you replace a with c).
May
7
answered Inverse Identity + Constant Matrix
May
7
answered Find the determinant of the following;
May
4
revised Rational Numbers and farey fractions
edited tags
May
4
answered Partial sums for a power series