If the product of some prime numbers is ± 1, the resulting number cannot be divisible by these prime numbers Is there any proof? If the product of some prime numbers is ± 1, the resulting number cannot be divisible by any of these prime numbers.

If the product of some prime numbers is ± 1, the resulting number cannot be divisible by these prime numbers Is there any proof? If the product of some prime numbers is ± 1, the resulting number cannot be divisible by any of these prime numbers.

The proof of: there are n prime numbers P1, P2 Their product is s = P1P2P3 Let P n be k = s ± 1, assuming that PI can divide K (I = 1,2,...) n) So PI divides P1P2P3 PN ± 1 and PI divising P1P2P3 Therefore, it is impossible to assume that PI can't divide K, so the product of some prime numbers