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Some fun answers of mine:
A real number $x$ such that $x^n$ and $(x+1)^n$ are rational is itself rational
A series of rationals whose every subseries is irrational
Is every rigid field perfect?
Prove $\sum^{\infty}_{n=1} \frac{a_{n+1}-a_{n}}{a_{n}}=\infty$ for an increasing sequence $a_n$ of positive integers
The prime spectrum of a Dedekind domain
A fun integral
The same integral, solved in another way
All elements in $\mathbb{Z}/n\mathbb{Z}$ are representable as sum of a square and a cube?
Algebraic varieties in $\mathbf C^n$ have no interior points
A function with a critical point