Question

Given a set of numbers, each of them greater then 1, none of them divides one more than their product.

Answer 1

Answer: So the set is X > 1, X ⊂ N

so x ∈ X = {2,3,4,5.....}

So the statement is, if x.y ∈ X

then x cant divide (x*y +1)

you can see this using the distributive property in the next way:

`(x*y + 1)/(x)  = (x *y)/(x)  + (1)/(x)  = y + (1)/(x)`

where y is a natural, and 1/x is a irrational number, the addition of a natural and a irrational number is an irrational number.

then
`(x*y + 1)/(x)` is irrational, this means that x does not divide x*y +1.