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Dec
10
comment Cutesy Applications of Fermat's Last Theorem (or others)
From the other part of the product $(a^n-b^n)^2+(b^n+c^n)^2+(a^n+c^n)^2 = 0$.
Dec
10
comment Cutesy Applications of Fermat's Last Theorem (or others)
One of the factors given by the equation is $a^n+b^n-c^n$ which by FLT is never zero.
Nov
17
comment Proving that a Finite Field Over Its Prime Field Is Galois
I don't remember making this review. Galois theory is not among my favorite subjects neither... Maybe your answer got mixed up with something because it is too short, like a comment.
Nov
15
comment Minimizing $\int_{0}^{1} (1+x^2)f(x)^2 dx$ for $f(f(x)) = x^2$
@mick: No one's voting to close because a source is missing, but the fact that you are the source and you don't know the solution is not very encouraging. I asked since some problems taken from high profile contests or exercices from advanced books are not easily solved if you don't have some context. Furthermore, if you just made up the problem, it may not even be possible to solve it...
Nov
15
comment Minimizing $\int_{0}^{1} (1+x^2)f(x)^2 dx$ for $f(f(x)) = x^2$
What's the source of this problem?
Nov
15
comment Minimizing $\int_{0}^{1} (1+x^2)f(x)^2 dx$ for $f(f(x)) = x^2$
@AlfredYerger: I think $f^2$ means $f$ squared. If the superscript refers to composition like you say, then you just replace by $f\circ f$ by $x^2$ and you don't have anything to optimize.
Nov
15
comment How can you plot straight lines in Matlab using only values on x axis and the gradient of each line?
If you want any real help with your Matlab code you'd better write the whole code properly and then ask exactly what you need. You do not explain the mathematical problem and it is not really clear what you want the matlab program to do.
Nov
14
comment Proving that a Finite Field Over Its Prime Field Is Galois
This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
Nov
12
comment Polynomial with complex coefficients proof problem
The only case where a polynomial has infinitely many roots is where the polynomial is equal to zero everywhere. Then every number is a root. If a polynomial is not constant zero then it has finitely many roots.
Nov
12
comment Polynomial with complex coefficients proof problem
It doesn't matter if a polynomial has complex or real coefficients. The idea is that it can only have a finite number of roots. Thus, this is a useful fact that you can learn about polynomials: if a polynomial has infinitely many roots then it is the zero polynomial.
Nov
8
comment An isosceles trapezium
@kissanpentu: $E$ is the midpoint of $AP$ and the triangle $APQ$ is rectangle. This means that the triangle $EPQ$ is isosceles and the angles $EPQ$ and $EQP$ are equal. Since the angle $FQP$ is half the angle $APQ$ by hypothesis, it follows that it is also half the angle $EQP$ and thus $QF$ is the bisector of this angle.
Nov
6
comment Continuity of line integral as a function of path
@matb: Have you read my comment? If you only consider uniform convergence of the paths, the integrals are not continuous. For $f \equiv 1$, for example you only have lower semicontinuity, You should consider convergence in the $C^1$ norm if you want continuity.
Nov
5
comment Continuity of line integral as a function of path
The term $|\gamma'(s)|$ is not necessarily uniformly bounded. Take a sequence of high oscillating curves converging to $\gamma$. I guess this already gives you a counter example: Take $f \equiv 1$ so that you are, in fact dealing with the length of curves. It is known that length of curves is lower semicontinuous, but it is not necessarily continuous. Again, high oscillating curves may converge uniformly to a curve while having lengths which are much higher than the length of the limit curve.
Oct
23
comment Ask an optimization problem
Did you compute the optimality conditions? You intend to do numerical computations?
Oct
22
comment Continuity of Integral.
Why do they need to be disjoint? If you increase $n$ both sets increase and their intersection also increases.
Oct
21
comment Is there a relation between $ (x_1^TAx_1 +x_2^TAx_2)$ and $(x_1^TAx_2)$?
If $A$ is not symmetric then you cannot hope to find a relation. Notice that if a relation could be obtained then it would be symmetric in $x_1,x_2$ which means that $x_1^T A x_2 = x_2^T A x_1$.
Oct
21
comment Let $S$ be a countable set in $\mathbb R^2$. Prove that there exists a line that does not contain, any point from $S$.
Yes, of course.
Oct
21
comment Find the area of the triangle
You could enlarge the basis and diminish the height of the triangle so that it is not highly acute. In what sense do you plan to use affine maps to do this? What advantage do you get by performing such transformation?
Oct
10
comment Tangent line to a function at c that passes through the origin
It is a function that we can define starting from $f$.
Oct
10
comment Tangent line to a function at c that passes through the origin
$g(x)$ is not constant $b$. It has values $b$ just in the points $x_1,x_2$ and in between it may take other values. I don't understand your second comment. The answer works for every differentiable function $f$.