AMO 2027 Grades 8-9 SET 13 - Self-study Question 2

Question 43. If $N=2^A\times5^B\times101^C$, find the least value of $A\times B\times C$ so that $2020N$ is a perfect cube.

**Editorial input convention:** Use the prime-factorisation convention that A, B, C are nonnegative integers.