18 problems.
- Integral identity for \(x^{-x}\)
- A differential inequality with \(f(0)=0\)
- The largest open set disjoint from a subset
- A cosine power series
- Conformal map from a crescent to the disk
- Square root of a unipotent matrix
- Entry bound for a positive semidefinite matrix
- GCD distributes over LCM
- Cauchy’s theorem for elements of prime order
- Integral-test error for the Basel series
- A real polynomial forced to have a nonreal zero
- Continuous open maps \(\mathbb R\to\mathbb R\) are monotone
- The integral \(\int_{-\infty}^{\infty}(x-\sin x)/x^3\,dx\)
- Derivative at the origin for an extremal bounded entire function
- Strict diagonal dominance implies invertibility
- Multivariate Gaussian integral with a linear term
- No positive integer solutions to \(x^2+y^2=7xy\)
- Smallest symmetric group containing an element of order \(111\)