Intereting Posts

limit in probability is almost surely unique?
complex and decimal tetration
If a function can only be defined implicitly does it have to be multivalued?
Local vs. global in the definition of a sheaf
Obtaining Wirtinger presentation using van Kampen theorem
Primes as quotients
A general element of U(2)
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
conversion of laplacian from cartesian to spherical coordinates
Geometrical interpretation of $I(X_1\cap X_2)\neq I(X_1)+I(X_2)$, $X_i$ algebraic sets in $\mathbb{A}^n$
Prove that the numerator of $H_{p-1}$ in reduced form is a multiple of $p$ for $p$ an odd prime
Integral $\int_0^\infty \frac{\sin x}{\cosh ax+\cos x}\frac{x}{x^2-\pi^2}dx=\tan^{-1}\left(\frac{1}{a}\right)-\frac{1}{a}$
How do you prove this integral involving the Glaisher–Kinkelin constant
Less than or equal sign
Random $0-1$ matrices

Is it true that the product of $n>1$ consecutive integers is never a $k$-th power of another integer for any $k \geq 2$?

I can see this is true in certain cases. For instance if the product ends on a prime, But how would one prove this in general?

Thanks for any help or suggestions.

- Do these inequalities regarding the gamma function and factorials work?
- Bounds for Waring's Problem
- Find taxicab numbers in $O(n)$ time
- Prove that $5^{1/3}+7^{1/2}$ is irrational
- Find the value of $a^2-b^2+c^2$
- What is the max of $n$ such that $\sum_{i=1}^n\frac{1}{a_i}=1$ where $2\le a_1\lt a_2\lt\cdots\lt a_n\le 99$?

- Is it possible to generalize Ramanujan's lower bound for factorials when $\{\frac{x}{b_2}\} + \{\frac{x}{b_3}\} \ge 1$?
- Find primitive element such that conductor is relatively prime to an ideal (exercise from Neukirch)
- Find the value of $a^{2m}+a^m+{1\over a^m}+{1\over a^{2m}}$
- $\# \{\text{primes}\ 4n+3 \le x\}$ in terms of $\text{Li}(x)$ and roots of Dirichlet $L$-functions
- Bounding this arithmetic sum
- Questions concerning the Integration of Integer Tetration
- Why is every positive integer the sum of 3 triangular numbers?
- Number theory problem - show $N$ is a square when…
- What is the Pontryagin dual of the rationals?
- Is this division theorem already a proven idea?

Yes, this is true. This was proven by Erdős and Selfridge in this paper.

- Solving equations of form $3^n – 1 \bmod{k} = 0$, $k$ prime
- How did Archimedes find the surface area of a sphere?
- How to evaluate this improper integral $\int_{0}^{\infty}\frac{1-x}{1-x^{n}}\,dx$?
- Prove that $n^2+n+41$ is prime for $n<40$
- Complex Analysis Question from Stein
- How does $\cos(2\pi/257)$ look like in real radicals?
- A ring with few invertible elements
- Is it meaningful to take the derivative of a function a non-integer number of times?
- Is $n \sin n$ dense on the real line?
- Characterization convex function.
- What is a Real Number?
- Are there uncountably infinite orders of infinity?
- Proof about a Topological space being arc connect
- making mathematical conjectures
- Prove trigonometry identity for $\cos A+\cos B+\cos C$