18 problems.
- Similarity of two \(3\times3\) matrices with characteristic polynomial \((x-1)^2(x-2)\)
- Is \((5,x^3+x+1)\) a prime ideal of \(\mathbb Z[x]\)?
- Roots of \(2z^5+4z^2+1\) in the unit disk and on the real axis
- The solution of \(y''=-|y|\) with \(y(0)=1,y'(0)=0\) has exactly one positive zero
- Intersecting with a finite-index subgroup preserves finite index
- Completeness along a continuous surjection with \(d_1(p,q)\le d_2(f(p),f(q))\)
- The integral \(\int_{|z|=1} e^z/[z(2z+1)^2]\,dz\)
- An irreducible minimal polynomial controls cyclic-subspace dimensions
- Reality of a holomorphic function on both real rays outside the unit disk
- Sylow \(2\)-subgroups of a dihedral group of order \(2n\) for odd \(n\)
- Left and right radicals of a bilinear form have equal dimension
- Compactness from a singular derivative bound and zero mean
- The integral \(\int_{-\infty}^{\infty}\sin x/[x(1+x^2)]\,dx\)
- Global existence comparison for scalar autonomous ODEs
- Normal subgroups of an upper-triangular matrix group
- A proper local diffeomorphism \(\mathbb R^n\to\mathbb R^n\) is surjective — Fall 1992 Problem 16; repeated exactly as Spring 1980 Problem 16
- Harmonicity of \(r^s\cos(s\theta)\) on the slit plane
- Parameters for which every solution of a second-order recurrence has period \(k\)