关于Golomb猜想

Golomb猜想 :对奇素数 p,存在原根 g,h使 g + h≡ 1(mod p)。本文证明 :对奇素数 p,p -1的标准分解是 :p - 1=2αpα11… pαkk , r =∏ki=1(1- 1pi) ,则当α 2 ,r >0 .75时 。

Golomb conjectures that for odd prime p, there are two primitive roots g and h that make g+h≡1(mod p). This paper proves that for odd prime p, if the standard discomposition of p-1 is p-1=2 αp α 1 1...p α k k,\ r=∏ki=1(1-1p i), then the Golomb conjecture is true when α≥2,r >0.75. key words: guadratic residue; primitive root