Proof that any number is equal to $1$

Is there a good (non-calculational) reason for the formula $|v \times w|^2 + (v \cdot w)^2 = (|v||w|)^2$?

Dominated convergence theorem and Cauchy's integral formula

Integer solutions of $2a+2b-ab\gt 0$

Is $22/7$ the closest to $\pi$, among fractions of denominator at most $50$?

Showing that $a$, $b$, $c$, $d$ are in geometric progression iff $(a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+bc+cd)^2$

What is $f(x)$ if $f(x) +xf(-x)=x+1$?

Evaluate $\int \:\frac{3x^5+13x^4+32x^3+8x^2-40x-75}{x^2\left(x^2+3x+5\right)^2}\:dx$

L'Hopital's rule conditions

Does $\int _0^{\pi }e^x\sin ^n x\:\mathrm{d}x$ have a closed form?

Evaluate $\int_0^{\frac{\pi}{2}} \frac{\sin^3{(2x)}}{\ln{\left(\csc{x}\right)}} \mathop{dx}$

$3 \times 3$ matrix with determinant a large power of $2$

Are projective modules over $\mathbb{Z}[x_1,...,x_m]$ free?

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