18 problems.
- Limit of \((n^n/n!)^{1/n}\)
- Lebesgue number for a ball cover of a compact subset of \(\RR^n\)
- Integral of \(1/(2+\cos\theta)\) over \([0,2\pi]\)
- Five roots of \(\varepsilon z^7+z^2+1\) lie in a scaled annulus
- A nonzero nilpotent \(2\times2\) complex matrix has no square root
- Rational homogeneous systems with a complex solution have a rational solution
- Irreducibility of \(x^4+x^3+x^2+6x+1\) over \(\QQ\)
- Rightmost decimal digit of \(17^{17^{17}}\)
- Infinitely many pairwise nonisomorphic quadratic extensions of \(\QQ\)
- \(e^x>x^t\) for every \(x>0\) exactly when \(0<t<e\)
- If \(\varphi\) and \(\varphi'\) both have limits at \(\infty\), then \(\varphi'\to0\)
- The range of \(X\mapsto X+X^2\) contains a neighborhood of the zero matrix
- An analytic function with a nontrivial real linear relation between its real and imaginary parts is constant
- An exponential integral of a continuous function is entire in \(z\)
- A positive-semidefinite symmetric matrix anticommuting with another matrix has zero product
- Spectrum and determinant of the matrix with zero diagonal and ones off diagonal
- Faithful action of \(SL_2(\FF_4)\) on the projective line over \(\FF_4\)
- Automorphisms of a direct product of finite groups of coprime orders