Intereting Posts

Some questions about Hartshorne chapter 2 proposition 2.6
Prove or find a counterexample: For all real numbers x and y it holds that x + y is irrational if, and only if, both x and y are irrational.
If every subsequence ${a_{sn}}$ where $s>1$ is an integer converges , Then will $a_{n} $ converge?
Prove the following trigonometric identity without a calculator involved
Can you define a greatest common divisor in a commutative ring that is not a domain?
An ideal that is maximal among non-finitely generated ideals is prime.
cyclic vectors- cyclic subspaces
Interior Set of Rationals. Confused!
Reference request: proof that the first hitting time of a Borel set is a stopping time
I want to know why $\omega \neq \omega+1$.
How to find $P(n+1)$, given $P(x)$ for $x = 0,1,\ldots,n$?
Conditionally combining vanilla and chocolate ice cream scoops
Do there exist manifolds which cannot be smoothly embedded in a compact manifold?
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
Need help in proving that $\frac{\sin\theta – \cos\theta + 1}{\sin\theta + \cos\theta – 1} = \frac 1{\sec\theta – \tan\theta}$

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.

- Generalization of Dirichlet's theorem
- $\sum_{p \in \mathcal P} \frac1{p\ln p}$ converges or diverges?
- General formula to obtain triangular-square numbers
- Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
- Triangular Factorials
- Is it cheating to use the sign function when sieving for twin primes?

- Show that there exists infinitely many numbers that are coprime pairwise, in the set defined as following
- Why can no prime number appear as the length of a hypotenuse in more than one Pythagorean triangle?
- Motivation behind the definition of ideal class group
- Sequence of positive integers such that their reciprocals are in arithmetic progression
- How is $x^2 + x + 1$ reducible in $\mathbb{Z}_3$?
- If $\sigma(n) \equiv 2 \pmod 4$ and $n$ is odd, does this imply that $n = p^k m^2$?
- What is the *middle* digit of $3^{100000}$?
- LCM of binomial coefficients and related functions
- Can different tetrations have the same value?
- Fibonacci $\equiv -1 \mod p^2$

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

- Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$
- Find the angle of depression
- If $f$ is integrable then $|f|$ is also integrable
- Derivative at $0$ of $\int_0^x \sin \frac{1}{t} dt$
- Prove $C(A)=A\cup\partial A$.
- The dense topology
- Difference between Deformation Retraction and Retraction
- Is there an introduction to probability and statistics that balances frequentist and bayesian views?
- Proof that $\mathbb{R}^+$ is a vector space
- Prove that equation has exactly 2 solutions
- How do I prove that $\arccos(x) + \arccos(-x)=\pi$ when $x \in $?
- Induction to prove $2n + 3 < 2^n$
- How many Turing degrees are there?
- Practical method of calculating primitive roots modulo a prime
- Euler-Lagrange, Gradient Descent, Heat Equation and Image Denoising