Solution

37222

Problem / game
Tens Back to problem
First name
Lee Kyung Chan
School
Garden International School
Country
South Korea (Republic of Korea)
Age
15

1) n is odd number
9^n+1^n=(9+1)(9^(n-1)-9^(n-2)+...+1) (because n is odd number)
7^n+3^n=(7+3)(7^(n-1)-7^(n-2)*9+...+9^(n-1))

2) n is even number
8^n-2^n=8^2k-2^2k=64^k-4^k=(64-4)(64^(k-1)+...+4^(k-1))
6^n-4^n=6^2k-4^2k=36^k-16^k=(36-16)(36^(k-1)+...+16^(k-1))

So, all four numbers are divisible by 10.