MathNet 2019-part-06 — 184 problems (EN–VI) Question 62

Find all integers $k \gt 1$ satisfy condition: there exists some nonnegative integer $n$ such that the number $A = 17^{18n} + 4 \cdot 17^{2n} + 7 \cdot 19^{5n}$ can be written as the product of $k$ consecutive positive integers.