Consider 4-heap Game of Nim with heaps of sizes 26,18,14,12. (1) Is this game balanced? (2) Determine all winning moves for player I.

he Euler function (n), for any positive integer n, is defined to be the number of integers k in {1,2,,n} such that as the greatest common divisor of k and n is 1, i.e., gcd(k,n)=1. For example, since gcd(1,4)=1, gcd(2,4)=2, gcd(3,4)=1, gcd(4,4)=4, we have (4)=2. Please compute (6), (9) and (175).