## Square Product

#### Problem

Given that [`n`(`n`+1)(`n`+2)]^{2} = 3039162537*6, find the value of *.

#### Solution

In any three consecutive integers, `n`, `n`+1, `n`+2, at least one of the numbers will be even, and one of them will be a multiple of 3. Hence the product, `n`(`n`+1)(`n`+2), will be even and divisible by 3. Furthermore, the square of an even number will be divisible by 4, and the square of a multiple of 3 will be divisible by 9.

If a number is divisible by 9, the sum of the digits will also be divisible by 9: 3 + 3 + 9 + 1 + 6 + 2 + 5 + 3 + 7 + 6 = 45, so the value of * must be 0 or 9.

However, if the number is divisible by 4, the last two digits (either 06 or 96) must be divisible by 4. Hence the value of * is 9.

Find the value of `n`.

How would you solve the equation, [`n`(`n`+1)(`n`+2)]^{2} = `k`, in general?