2

Part of 2016 USAJMO

Problems(1)

I Got Six Consecutive Zeros on JMO!

Source: USAJMO 2016, Problem J2

Prove that there exists a positive integer

n < 10^6

5^n

has six consecutive zeros in its decimal representation.
Proposed by Evan Chen

AMCUSA(J)MOUSAJMO2016 USAJMO2016 USAJMO Problem 2