List questions from solution-verification

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Linear transform of jointly distributed exponential random variables, how to identify domain?

Exercise 7.19 from Papa Rudin: Gathering solutions

Proof verification: $\forall n \in \mathbb{Z}, 4\nmid(n^2+2)$

Proof verification: a function with finitely many points of discontinuity is Riemann integrable

Do Monoid Homomorphisms preserve the identity?

Cantor-Lebesgue's theorem

If $a$ is an integer, prove that $\gcd(14a + 3, 21a + 4) = 1$.

Number theory gcd

$|G| > 1$ and not prime implies existence of a subgroup other than two trivial subgroups

Prove/Disprove: Sum of im/ker of linear transformation contained in ker/im of each linear trasnfromation

Proof that the interior of any set is open

Closure in a topological group

Given $x = \sqrt[4]{x^{3}+6x^{2}}$, determine whether the sum of all possible roots of $x$ is equal to $1$.

How many different perfect matchings does $K_{n,n}$ have?

Looking for a proof of a weird Combinatoric identity I came across

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