The existence of $a,b$ such that $\int_a^b f(x)dx=\int_a^b g(x)dx=1/2$.
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
58832
How prove this $\int_{a}^{b}[f''(x)]^2dx\ge\dfrac{4}{b-a}$
54797
Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$
95626
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
104394
What does $\int_{a}^{b} f(x)$ mean?
33593
An example of a non-abelian group $G$ where, for all $a,b\in G$, the equality $(ab)^{n}=a^{n}b^{n}$ holds for two consecutive integers $n$
114982
How do I get that $|\int_a^b f| \le \int_a^b |f|$?
81799
Examples of functions where $f(ab)=f(a)+f(b)$
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
91775
Show that $\int_0^1 f^2(x)dx\geq 3$, if $f:[0,1]\to \mathbb{R}$ is an integrable function s.t. $\int_0^1 f(x)dx=\int_0^1 xf(x)dx=1$
107659
Let $f:A \to B$ and $g:B\to A$ be arbitrary functions.
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$