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May
30
comment Finding an expression to represent this pattern
You really need to tell us more about the source of these numbers. In particular, are the decimal numbers rounded or exact?
May
30
comment For all integrable $f:[-1,1]\mapsto \mathbb{R}$ prove that $\int_{-1}^1f^2(x)\ge\frac12(\int_{-1}^1f(x))^2+\frac32(\int_{-1}^1xf(x))^2$
Please spell Cauchy-Schwarz correctly.
May
30
comment little inequality conjecture
Please spell Cauchy-Schwarz correctly.
May
29
comment Is the area of a pentagon inscribed into an ellipse independent of starting point?
@DavidSpeyer It doesn't matter where the origin is, one can just add the five expressions.
May
28
comment Is the area of a pentagon inscribed into an ellipse independent of starting point?
Your link states: In the comments below, it is stated that this conjecture is not true. However, the comments are behind a login wall. Could you please tell us what the comments say?
May
25
comment Number of non-decreasing sequences
@vonbrand But once is less than twice, so it is not most frequent.
May
25
comment Number of non-decreasing sequences
Do you have a conjecture?
May
21
comment End of undergraduate college. What to study next?
What did YOU find most interesting among your undergraduate subjects?
May
20
comment math student looking to do better in math competitions.
This information is insufficient to give you good advice. How much of an effort are you willing to make? Do you know any undergraduate mathematics? What does it mean for your knowledge and ability to get a silver medal in your country? Could you solve IMO problems? Have you even looked at IMC problems before? I am a great fan of competition mathematics, but I really would not advice anyone to prepare for a competition who did not enjoy the preparation for its own sake.
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
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
7
comment Inverse Identity + Constant Matrix
That is correct (if you replace a with c).