let n≥2 be an integer.prove that n is prime if and only if for every integer a,either hcf(highest common factor) (a,n)=1 or a|n

let n≥2 be an integer.prove that n is prime if and only if for every integer a,either hcf(highest common factor) (a,n)=1 or a|n
let n≥2 be an integer.prove that n is prime if and only if for every integer a,either hcf(highest common factor) (a,n)=1 or a|n

let n≥2 be an integer.prove that n is prime if and only if for every integer a,either hcf(highest common factor) (a,n)=1 or a|n
要证明的应该是这样一个题目
n≥2的整数有且仅有一个n对于任一整数a,最大公因数为1或a|n
如果两个数互质,则最大公因数为1
如果两个数不互质,a|n,那最大公因数应该是n才对啊