2 problems

Let $n,m\in\mathbb{N}$ satisfy $n>2$, $\lfloor\log_2(n)\rfloor+1\geq m>1$, and suppose there is no $k\in\mathbb{N}$ such that $k^m=n$. Then Shunia's conjecture. … The formula gives…

Let $a,n\in\mathbb{Z}^+$ satisfy $a>2$, $\left\lfloor\log_2(a)\right\rfloor+1\geq n>1$, and suppose there is no $k\in\mathbb{Z}^+$ such that $k^n=a$. Integer-part root conjecture.…