The sum of four consecutive positive even integers is a perfect square. What is the least possible sum?
I know that any even integer can be written as 2k, where k is a positive integer. So the sum of four consecutive even integers would be 2k + 2(k+1) + 2(k+2) + 2(k+3), which simplifies to 8k + 12. This means I want to find the smallest k such that 8k + 12 is a perfect square. If k = 1, then 8k + 12 = 20, which is not a perfect square. If k = 2, then 8k + 12 = 28, which is not a perfect square. If k = 3, then 8k + 12 = 36, which is a perfect square. So the smallest possible sum is 36, and the four consecutive even integers are 6, 8, 10, and 12.

