18 problems.
- Limit of \(\alpha\int_0^1 x^{\alpha-1}f(x)\,dx\) as \(\alpha\to 0^+\) — Problem 1A
- Real matrices with \(X^2=-I\) have even size — Problem 2A
- Polynomial growth forces a meromorphic function to be rational — Problem 3A
- Counting commuting tuples in a finite group via conjugation orbits — Problem 4A
- Stable rotation of a four-legged table on an uneven floor — Problem 5A
- Dimension of the centralizer of a \(2\times 2\) complex matrix — Problem 6A
- Evaluation of \(\int_0^\pi d\theta/(a+\cos\theta)\) by residues — Problem 7A
- Fixed field of \(x\mapsto x^{-1}\) on \(\mathbb Q(x)\) — Problem 8A
- Lower bound \(\operatorname{lcm}(1,\dots,2m+1)\ge 2^{2m}\) via \(\int_0^1 x^m(1-x)^m\,dx\) — Problem 9A
- Higher derivative test for local extrema — Problem 1B
- \(BA-AB=A\) forces \(A\) nilpotent in characteristic zero — Problem 2B
- Counting roots of \(z^4-5z^3+z-2\) in a disk — Problem 3B
- Inverses in \(\mathbb Q(\alpha)\) are polynomials in \(\alpha\) — Problem 4B
- Asymptotics of the Newtonian potential of a compactly supported function — Problem 5B
- Courant–Fischer min-max characterization of eigenvalues — Problem 6B
- Odd univalent function \(\sqrt{f(z^2)}\) from a normalized univalent \(f\) — Problem 7B
- Centers of nonabelian groups and \(p\)-groups; groups of order \(p^2\) are abelian — Problem 8B
- \(\sin nx\) has no pointwise convergent subsequence — Problem 9B