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34
using numbers 1 to 9 only once to equal 1 million
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30
Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group
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26
Conjugate class in the dihedral group
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24
Is it true that a continuous function with compact support is uniformly continuous?
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22
1 and 2 norm inequality
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21
Series with factorial.
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18
Let $f \in \Bbb Z[x]$ such that there exist distinct $a$, $b$, $c$ and $f(a)=f(b)=f(c)=1$. Prove that there is no $d \in \Bbb Z$ such that $f(d)=0$
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17
Lim inf with norm and weak convergence
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16
Polynomial always non-negative
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15
Prove that $4x-x^4 \leq 3, x \in \Bbb R$
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13
$55$ gangsters shoot the nearest gangster to them, where all the distances between them are different. Prove that at least one gangster will survive.
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13
Prove inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{9\sqrt[3]{abc}}{a+b+c}\geq 6$
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13
How to prove $\sum_{k=0}^\infty \frac{2^k}{2^{2^k}+1}=1$?
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13
problem proving: $(1+q)(1+q^2)(1+q^4)...(1+q^{{2}^{n}}) = \frac{1-q^{{2}^{n+1}}}{1-q}$
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13
Why is every answer of $5^k - 2^k$ divisible by 3?
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12
Find $ \lim_{n\rightarrow \infty} \frac{1}{n^2} + \frac{2}{(n+1)^2}+\dots+\frac{n+1}{(2n)^2} $
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12
Prove that there exists a sequence $(x_n)$ such that $\sum_n a_n x_n$ diverges
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12
Let $N$ be a normal subgroup of index $m$ in $G$. Prove that $a^m \in N$ for all $a \in G$.
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12
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
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11
what are the zeroes of $f(x) = 2^x + 3^x - 5^x?$
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11
What are different ways to prove that $\sum_{n=1}^{\infty}\frac 1n$ is divergent?
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11
$\frac{(a^2+b^2)}{(1+ab)}$ must be a perfect square if it is an integer
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11
Prove that $n(1+n)^{\frac{1}{n}} < n+H_n$ for every $n \geq 2$.
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10
Is $x^4+4$ an irreducible polynomial?
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10
Prove that $ 1+2q+3q^2+...+nq^{n-1} = \frac{1-(n+1)q^n+nq^{n+1}}{(1-q)^2} $
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10
Solving functional equation $f(x+y)=f(x)+f(y)+xy$
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10
Prove $\sum^{\infty}_{n=1} \frac{a_{n+1}-a_{n}}{a_{n}}=\infty$ for an increasing sequence $a_n$ of positive integers
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9
$P=1+X+X^n$, $n\in \mathbb{N}$ has only simple roots
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9
Evaluate the following limit: $\lim_{n\to\infty}\left(\sum_{r=1}^{n}{\frac{r}{n^{2}+n+r}}\right)$
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9
If $f(f(x)) = -x$ then is $f$ continuous?
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