NUMBERS HAVING M SMALL MTH ROOTS MOD P

Here are two typical results about the numbers mentioned in the title: If p is a prime such that p = 1 (mod 6) and p > 67, then there are ex actly six numbers mod p, each of which has six sixth roots less than 2 square-root 3p in absolute value. If p is a prime such that p = 1 (mo d 8), then there is at least one number mod p which has eight eighth r oots less the p3/4 in absolute value.