Intereting Posts

Large product of matrices equal zero but not small ones
If $X$ and $Y$ are independent then $f(X)$ and $g(Y)$ are also independent.
Find all natural values n, that $\sqrt{P_{2}(n)}$ is also a natural number
Why is there a difference between a population variance and a sample variance
How to show that geodesics exist for all of time in a compact manifold?
How to choose between two options with a biased coin
why does the reduced row echelon form have the same null space as the original matrix?
Find the sum of $-1^2-2^2+3^2+4^2-5^2-6^2+\cdots$
If $a,b$ are integers such that $a \mid x$ and $b \mid x$ , must $\mathrm{lcm}(a,b)\mid x$?
Ring isomorphism for $k(G \oplus \mathbb Z )$ with $G$ torsion-free and abelian
Is every function between finite sets a restriction of a morphism of finite abelian groups (up to bijection)?
How I can decompose $\ln(3f(x)+2g(y))$
Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
Finite Series $\sum_{k=1}^{n-1}\frac1{1-\cos(\frac{2k\pi}{n})}$
Functions that take rationals to rationals

I am trying to find all positive integer solution $(x,y,z)$ of equation $x^4+5y^4=z^4$.

Here I fould: $(x,y,z)=(1,2,3)$ and $(d,2d,3d)$. I try to prove if $(x,y)=1$ then $(1,2,3)$ is the unique solution of equation. Could anyone help me for this question?

- A triangle determinant that is always zero
- Infinitely many primes of the form $pn+1$
- Maximum distance between points in a triangle
- Connecting square vertexes with minimal road
- Coloring $\mathbb R^n$ with $n$ colors always gives us a color with all distances.
- $\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.

- If $f$ is a strictly increasing function with $f(f(x))=x^2+2$, then $f(3)=?$
- Shortest distance between two circles
- Prove by elementary methods: the plane cannot be covered by countably many copies of the letter “Y”
- How many 0's are in the end of this expansion?
- $a+b=c \times d$ and $a\times b = c + d$
- Prove that there are infinitely many natural numbers $n$, such that $n(n+1)$ can be expressed as sum of two positive squares in two distinct ways.
- Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
- $ x^2 + \frac {x^2}{(x-1)^2} = 2010 $
- find a parametric solutions for a special equation
- Closed form for $\sum_{n=0}^\infty\frac{\operatorname{Li}_{1/2}\left(-2^{-2^{-n}}\right)}{\sqrt{2^n}}$

- General McNugget problem
- Show that a collection of Borel-subsets are Borel.
- $\dfrac{(x-1)(x+1)}{ (x+1)} \rightarrow (x-1)$ Domain Change
- The product of all the conjugates of an ideal is a principal ideal generated by the norm.
- $ \lim x^2 = a^2$ as $x$ goes to $a$
- Introductory text for calculus of variations
- Borel-Cantelli Lemma “Corollary” in Royden and Fitzpatrick
- Prove $f $ is identically zero
- Solution of $\frac{d^2y}{dx^2} – \frac{H(x) y}{b} = H(-x)$
- For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
- Intersection of nested closed bounded convex sets in Euclidean space
- Logical Form – Union of a Set containing the Power Set with Predicate/Propositional Function
- Accessing elements of packed symmetric distance matrix
- Cannabis Equation
- Are vector spaces and their double duals in fact equal?