This article attempts to use the proof methods of reduction to absurdity and classification discussion to provide the strict proofs for"there are infinite primes in the form of 8k+1(k∈Z)","there are infinite primes in the form of 8k-1(k∈Z)","there are infinite primes in the form of 8k+3(k∈Z)",and"there are infinite primes in the form of 8k-3(k∈Z)".The used knowledge is the fundamental knowledge in elementary number theory,limited to some basic properties of prime number,integer division,congruence,and Legendre symbol.To prove the main conclusions,this article first derives two very useful lemmas.
关键词
反证法/素数/整除/同余/Legendre符号
Key words
reduction to absurdity/prime number/exact division/congruence/Legendre symbol
维普
万方数据