New posts in algebra-precalculus

The existence of partial fraction decompositions

Sum of the first integer powers of $n$ up to k

High School Advanced Functions: Clarifying log rules in a log equation - $\log(x^2) = 2$, Solve for x.

IMO 2011: Prove that, for all integers $m$ and $n$ with $f(m)<f(n)$, the number $f(n)$ is divisible by $f(m)$

If $x;y$ $\in T$($x$ and $y$ can be the same), then $x^2-y \in T $ Prove that : $T = \mathbb Z $

Should the domain of a function be inferred?

Prove $\log_5{30}<\log_8{81}$

Positive integer solutions of $\frac{1}{a_1}+\frac{2}{a_2}+\frac{3}{a_3}+\cdots+\frac{n}{a_n}=\frac{a_1+a_2+a_3+\cdots+a_n}{2}$

Solve the trigonometric equation $4\tan(3x)=-3\tan(4x)$

Trigonometric inequality $ 3\cos ^2x \sin x -\sin^2x <{1\over 2}$

A conjecture regarding products of $u(x)=x+\frac1x$

Find the limit given that $f(1)=1$, $f(x+y)=f(x)+f(y)+2xy$ and $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^4}$

How find the value of the $x+y$

Value of $\sin (2^\circ)\cdot \sin (4^\circ)\cdot \sin (6^\circ)\cdots \sin (90^\circ) $

Find all function $f(n)$ satisfying $f(n)^2 = n f(f(n))$

Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $

Using trig identity to solve a cubic equation

Integral $\int\frac{\sin^4 x + \cos^4 x}{\sin^3 x + \cos^3 x} dx$

How does $2^{(\log_4{x})}$ become $\sqrt[2]{x}$?

Counting ten-digit numbers whose digits are all different and that are divisible by $11111$