Mike's user avatar
Mike's user avatar
Mike's user avatar
Mike
  • Member for 6 years, 1 month
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17 votes
Accepted

If $\sum_{n=1}^{\infty}{a_{[f(n)]}}$ converges, then $\sum_{n=1}^{\infty}{\frac{a_n}{f(n)}}$ converges.

11 votes
Accepted

What kind of mathematical rule was broken in here?

10 votes
Accepted

how do I compare those two logs?

10 votes
Accepted

Are there sequence $(u_n)\subset \mathbb R^+$ s.t. $\sum_{n=1}^\infty u_n<\infty $ but $nu_n\not\to 0$?

10 votes

Australian Math Competition Problem

9 votes
Accepted

Each group of order 8 has a subgroup of order 2 and a subgroup of order 4.

8 votes
Accepted

$n$ lines in a plane, proper coloring of intersection points with just 3 colors

8 votes

How can a finite set not have a maximum or minimum?

7 votes

Contest math problem about crossing out numbers in the table

7 votes
Accepted

Integers $1,2,...,n$ are placed in a way that each value is either bigger or smaller than all preceding values. In how many ways this can be done?

7 votes
Accepted

Why $P(x) = 0$ is equivalent to $\dfrac{P(x)}{P'(x)} = 0$ for every polynomial $P$?

6 votes

Why there is no formula log(a) * log(b) = (something)?

6 votes
Accepted

If an n x n matix A is not invertible, then is 0 an eigenvalue of A?

6 votes

Given $8\sqrt{p} = q\sqrt{80}$, where $p$ is prime, is the solution unique?

6 votes
Accepted

Finding the smallest possible $n$ such that $S_{n}$ has an element of a given order.

6 votes
Accepted

Is it possible to compute $-\log\left({\sqrt{1.8\times 10^{-5}\times 0.1}}\right)$ without a calculator?

6 votes
Accepted

Given a continuous function. Show that there exists x,y with x is not y so that f(x)=f(y)

6 votes
Accepted

Suppose $|G| < \infty$ and $H \leq G$ such that the product of any two left cosets has the same cardinality as $H$. Is $H$ is normal?

6 votes

Notice that $\sqrt{51}\approx 7+\frac{\sqrt{2}}{10}$

6 votes

If $G$ is a non cyclic group of order 27 find the number of elements $x\in G$ such that $x^9 = e$.

5 votes
Accepted

Find all $(p,n)$ s.t. $p+n\mid pn $

5 votes

Prove that the product $\prod_{i=1}^n\left(a_i+b_j\right)$ is also constant for all $j$.

5 votes
Accepted

Product of first $k$ primes compared to $p_{k+1}^2$

5 votes

Is the integral $\frac{1 + \cos x}x$ convergent or divergent?

5 votes
Accepted

Let $k$ be an odd integer. Let $A$ be a matrix such that $A^k = A + I$. Prove that $\det(A) > 0$.

5 votes
Accepted

How many solutions can $x^4=-1$ have on a field of characteristic $0$?

5 votes

Every natural number $n$ can be written as $n=s-t$ with $\omega(s)=\omega(t)$

5 votes
Accepted

What is the asymptotic form for the sum of the reciprocals of the first $n$ primes?

5 votes

Triangle free graph with $n$ vertices and maximum degree $k$ has at most $k(n-k)$ edges.

5 votes
Accepted

Prove that every undirected graph has some orientation that is a Directed Acyclic Graph.

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