An infinite sequence of primes p is formulated, and for each p polynomials of formaxn+b, (a, p)=(b, p)=1, are indicated such that $$\sum\nolimits_{x = 1}^p {\left( {\frac{{ax^n + b}}{p}} \right) = p,n \asymp \frac{p}{{log p}}.}$$