Final answer:
If the expression 5n + 3 is odd, then n must be an even integer when n is any integer, because the formula must yield an even result to keep 'n' an integer after dividing by 5.
Step-by-step explanation:
If n is an integer and 5n + 3 is odd, then n must be even. To see why this is the case, let's understand that any odd number can be written as 2k + 1, where k is an integer. The expression 5n + 3 can thus be written as 2k + 1 since it is odd. If we solve 5n + 3 = 2k + 1 for n, we subtract 3 from both sides to get 5n = 2k - 2, and then divide by 5 to get n = (2k - 2) / 5. For n to be an integer, k has to be such that (2k - 2) is a multiple of 5. As multiples of 5 are even, (2k - 2) is even, and thus n is also even since a division of an even number by another even number yields an even quotient.