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.
There is only 1 value of N that satisfies 2029 x N has exactly three divisors: N = 2029 To have exactly three divisors, the number must be the square of a prime number. 2029 is a prime number with exactly 2 divisors (1 and 2029). Thus the only number with exactly three divisors of which two are 1 and 2029 is 20292 (= 4116841), making N = 2029.
The sign of the product of four integers depends on the signs of the individual integers. There are 4 cases: 1) When all 4 integers share the same sign and all are non-zero (either all are positive or all are negative), the product is positive. 2) When 3 of the 4 integers share the same sign and all are non-zero (3 are positive and 1 is negative; or 3 are negative and 1 is positive)…
A product of two integers is those two numbers multiplied together. If the product is two integers, it is called a square. Two negative integers are multiplied together by multiplying them together just as if they are positive. For example, -3x-3=9. It is exactly the same thing as squaring a positive integer.