This question is duplicate of this.But it was solved by number theory and we have not been taught.I wonder if this can be solved by using Binomial theorem?
If $m,n \in \mathbb{N}$ such that $m<n$ and the last three digits of $(2978)^m$ and $(2978)^n$ are same then the question is to find out the least value of $m$ and $n$
I understand $$(2978)^n-(2978)^m=1000k$$for some positive $k$. I also understood that m,n should be greater than equal to 3. By binomial theorem i found that last three digits of $(2978)^n,(2978)^m$ are equivalent to that $(978)^m and(978)^n$. How to do further?