18 problems.
- A finite abelian group is generated by its elements of maximal order
- \(0\le f'\le Mf\) and \(f(0)=0\) imply \(f\equiv0\)
- An upper-triangular real matrix commuting with its transpose is diagonal
- \(\abs{f(z)}\le(1-\abs{z})^{-1}\) on the unit disk implies \(\abs{f'(0)}\le4\)
- The commutator subgroup centralizes a cyclic normal subgroup
- A fixed-distance locus from a closed subset of \(\mathbb R^n\) is closed
- A commuting diagonalizable operator is diagonalizable on each eigenspace
- The integral \(\int_0^\infty \log x/(1+x^2)\,dx\)
- Every intermediate subring \(F\subset R\subset F[x]\) is finitely generated over \(F\)
- Limit of the recurrence \(x_{n+1}=\alpha x_n+(1-\alpha)x_{n-1}\)
- Divisibility of \(\varphi(a^k-1)\) by \(k\)
- Factorization \(f=z^ne^g\) of a zero-free holomorphic function on an annulus
- \(A^TA\) and \(A^T\) have the same range
- \(\abs{f(x)-f(y)}\le M\abs{x-y}+\varepsilon\) for continuous \(f\) on a compact set
- Free groups of ranks \(2\) and \(3\) are not isomorphic
- A sparse polynomial of degree \(47\) has a zero in the unit disk
- A finite-dimensional vector space in characteristic zero is not a finite union of hyperplanes
- Arclength bound for a concave graph on \([0,1]\)