this question seems a bit strange.

the question says n is a positive integer, means n can be 1,2,3,4,....

if n=1, then 1x(1+42) = 43, and 43 is a prime number.

however, if n is any other positive integer, then n(n+42) divided by n gives quotient (n+42).

for example, if n = 5 ...
5x(5+42) = 5 x 47 = 235, which can be divided by 5 again to give back 47, so 235 is composite.

n x (n+42) is prime only for n=1,
but is composite for any other positive integer n.

Thanks for your detailed reply.

I think the question was intended to be a prime question.

Normally the question goes like this.

If n (n + 42) is a prime number, find the possible value(s) of n.