奇素数一个性质的推广及其应用

The Generalization of a Property of an Odd Prime and Its Applications

设n是大于1的奇数,q是n的最小素因数,证明了n-1∑j-1jq-1≡-n/q(modn).利用该结果改进了判别素数的一个充要条件,提出并证明了Giuga猜想的对偶命题.

Let n be an odd number greater than 1, and q the least prime divisor of n. It is proved in this paper that n-1∑j-1jq-1≡-n/q（mod n）. The result is used to improve a necessary and sufficient condition of criterionfor primes, and the dual proposition of Giuga＇s Conjecture is formulated and proved as well.