There are none because two consecutive even integers would add up to an even number and the number given of 217 is an odd number.
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The numbers are -53 and -52.
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
Try it out! Calculate the squares of some small integers! That shouldn't take too long.
Call the numbers 2n, 2n+2, and 2n+4 for some integer n. Using the form 2n ensures the numbers are even and adding 2 to the first one to get the second and then adding 2 to the third one to get the third ensures they are consecutive. Their sum is 54 so 6n+6=54 -> 6n=48 and n=8 The numbers are: 16, 18, and 20
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.