Intereting Posts

Summation by parts of $\sum_{k=0}^{n}k^{2}2^{k}$
Is the indicator function of the rationals Riemann integrable?
Starting digits of $2^n$.
Solve $A^nx=b$ for an idempotent matrix
show that: $f$ is injective $\iff$ there exists a $g: Y\rightarrow X$ such that $g \circ f = idX$
Chain rule for matrix exponentials
Does measurability/continuity of a mapping follow that of its sections?
Certain products of mostly diagonal matrices are nonzero
Unique Decomposition of Primes in Sums Of Higher Powers than $2$
Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists?
Smallest square containing a given triangle
Examples of open problems solved through short proof
Is there a Dihedral group of order 4?
n people & n hats: probability that at least 1 person has his own hat
Question on group homomorphisms involving the standard Z-basis

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?

- combinatorics olympiad problem - sort out a schedule
- Straightedge-only construction of a perpendicular
- For what $n$ is it true that $(1+\sum_{k=0}^{\infty}x^{2^k})^n+(\sum_{k=0}^{\infty}x^{2^k})^n\equiv1\mod2$
- Unique pair of positive integers $(p,n)$ satisfying $p^3-p=n^7-n^3$ where $p$ is prime
- No primes in this sequence
- Reference for combinatorial game theory.

- Generalizing Ramanujan's cube roots of cubic roots identities
- Do there exist an infinite number of integer-solutions $(x,y,z)$ of $x^x\cdot y^y=z^z$ where $1\lt x\le y$?
- Prove that $\vert\sin(x)\sin(2x)\sin(2^2x)\cdots\sin(2^nx)\vert < \left(\frac{\sqrt{3}}{2}\right)^n$
- Olympiad Inequality Problem
- A functional relation which is satisfied by $\cos x$ and $\sin x$
- Want less brutish proof: if $a+b+c=3abc$ then $\frac1a+\frac1b+\frac1c\geq 3$
- Diophantine equation: $7^x=3^y-2$
- Integers can be expressed as $a^3+b^3+c^3-3abc$
- Find minimum of $P=\frac{\sqrt{3(2x^2+2x+1)}}{3}+\frac{1}{\sqrt{2x^2+(3-\sqrt{3})x +3}}+\frac{1}{\sqrt{2x^2+(3+\sqrt{3})x +3}}$
- Solve $x^p + y^p = p^z$ when $p$ is prime

- How many different arrangements?
- Integrating $\int_0^{\pi/2}\log^2(\sin^2x)\sin^2x{\rm d}x$
- The length of an interval covered by an infinite family of open intervals
- Analytic function in the punctured plane satisfying $|f(z)| \leq \sqrt{|z|} + \frac{1}{\sqrt{z}}$ is constant
- Nilpotent matrices over field of characteristic zero
- Why do you add +1 in counting test questions?
- Find $C$ such that $x^2 – 47x – C = 0$ has integer roots, and further conditions
- How prove this $\lim_{n\to \infty}\sin{n^m}$ divergent.
- Sylow questions on $GL_2(\mathbb F_3)$.
- Maximum of $a_1 \cdot a_2 \cdots a_n$ given $a_1 + \cdots + a_n = 1000$?
- probability density of the maximum of samples from a uniform distribution
- Indefinite Integral with “sin” and “cos”: $\int\frac{3\sin(x) + 2\cos(x)}{2\sin(x) + 3\cos(x)} \; dx $
- Finding center and radius of circumcircle
- Partition problem for consecutive $k$th powers with equal sums (another family)
- Is there an analogue of Lebesgue’s Dominated Convergence Theorem for a net $ (f_{\alpha})_{\alpha \in A} $ of measurable functions?