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BMO-2 (2019)

*Prove that the product of four consecutive positive integers increase by one is a perfect square*

*Rephrased*


Given three consecutive positive integers,
The sum of the smallest positive integer raised to the first power, the middle positive integer raised to the second power and the largest positive integer raised to the third power is a perfect square.

The square root of the sum is equal to the sum of the three consecutive positive integers. Find the three consecutive positive integers.