How do you find all positive integers N such that the product 2029 x N has exactly four divisors?

2029 is a prime number. So let N be any prime number other than 2029.

Then 2029*N has the four factors 1, 2029, N and 2029*N.

[If N = 2029, then 2029 and N are the same and you have only 3 factors.]

So in theory you can find N. However, since there are infinitely many prime numbers, you cannot find them all.