20 problems.
- The integral \(\int_0^\infty \log x/(a^2+x^2)\,dx\)
- Number of conjugacy classes in a \(p^4\)-group with center of order \(p^2\)
- A differential inequality with zero boundary data forces nonpositivity
- \(\pi^3\) versus \(3^\pi\)
- A spectral relation \(AB=BA^2\) forces a common eigenvector away from the unit circle
- Convergence criterion for the iteration \(x_{n+1}=a+x_n^2\)
- Roots of \(z^7-4z^3-11\) in the annulus \(1<|z|<2\)
- A linear system with a trajectory decaying forward and diverging backward
- Rational linear systems solvable over \(\mathbb C\) are solvable over \(\mathbb Q\) — Problem 9
- Product and intersection of comaximal ideals in a PID
- Real matrices similar over \(\mathbb C\) are similar over \(\mathbb R\) — Problem 11
- Backward convergence to zero for \(y'=y-\sin y\) near the equilibrium
- A second-order expansion using \(\sin x\) as the local parameter
- Maximal ideals in the ring of functions on a finite set
- Cauchy transform of a continuous function on \([0,1]\) and its Laurent coefficients at infinity
- An invertible complex matrix with a diagonal power is diagonalizable
- Rational Taylor coefficients of \(z/(e^z-1)\)
- One-sided limits everywhere imply at most countably many discontinuities
- Monotonicity and endpoint limits of \(x\log(1+1/x)\)
- Finitely generated abelian groups with finite automorphism group