The difference depends on the integers. If the first integer is greater than the second then difference is positive. If the first integer is less than the second then difference is negative.
For example 6-4 = +2; 4-6 = -2
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Positive integers
It is negative.
It may be either. If any of the integers is zero, the product will be zero. Else, if one or three of the integers is negative, the product will be negative. Otherwise, it will be positive.
If there is any zero in the set of integers, their product is zero.If there is an odd number of negative integers, then the product is negative, whereas if there is an even number of negative values, the product is positive.
There is no such thing as consecutive numbers because numbers are infinitely dense. Between any two numbers there is another and so there is no such thing as a "next" number.There are no integers (square or non-square) between any two consecutive integers. There are infinitely many numbers between any two consecutive integers and, if the integers are non-negative, every one of these will be a square of some number so the answer is none. If the integers are negative then the infinitely many numbers will have a square root in the complex field but not in real numbers. In this case the answer is either none or infinitely many, depending on the domain.