Does $a(a^{-1} \bmod b) + b(b^{-1} \bmod a)

Is there an elegant way to take a derivative of this linear algebra problem?

Why do engineers use derivatives in discontinuous functions? Is it correct?

Alternative ways to evaluate $\int_0^1 x^{2n-1}\ln(1+x)dx =\frac{H_{2n}-H_n}{2n}$

If $A \times B$ is a Lie group, are both $A$ and $B$ Lie groups?

finding bounds for $\int_0^X\lfloor x^2\rfloor \, dx$

Inverse of a matrix and matrix relation

Proving that a Gaussian integer $a+bi$ with $a,b\neq0$ is composite in $\mathbb{Z}[i]$ if its norm $a^2+b^2$ is composite in $\mathbb{N}$?

Solve $ay''+by+c=0$ using separation of variables

Eliminating all removable discontinuities

Does the unit generate the additive group in a unital ring with cyclic additive group?

Does there exist a non-commutative algebraic structure with the following properties?

$f(x),g(x)$,2 quadratic polynomials:$|f(x)|≥|g(x)|∀x ∈ R$. Find the number of distinct roots of equation $h(x)h''(x)+(h'(x))^2=0$ if $h(x)=f(x)g(x)$

Does $a(a^{-1} \bmod b) + b(b^{-1} \bmod a) < ab + 2$ hold?