The first digit is the same

Number Theory Level pending

If $2^{n}$ and $5^{n}$ start with the same digit (where $n$ is a positive integer), what is that digit?

1 solution

Toshit Jain
Mar 3, 2017

If n=5 , 2^{5}=32 and 5^{5}=3125 . So, the common digit is 3

Can you prove that 3 is the only possible common digit? Hint: $2^{n}\times 5^{n}=10^{n}$

Freddie Hand - 4 years, 3 months ago