Junior Serbian Math Olympiad 2016 2

Number Theory Level 4

Find the minimal number of natural positive divisors of the number $|2016^{n}-36^{m}|$ , where $n$ and $m$ are positive integers .

1 solution

Rishabh Tiwari
May 22, 2016

We must have the given no. As smallest possible...hence we look out for

2016 - (36)^2 = 720, which has 30 factors. I did it by hit & trial so I request someone to please post a reasonable solution! Thank you!