MathNet 2019-part-05 — 184 problems (EN–VI) Question 5

Prove that for any real numbers $a_1, a_2, \dots, a_n$, $n \in \mathbb{N}$, there exists a real number $x$ such that the numbers $x + a_1, x + a_2, \dots, x + a_n$ are all irrational.