MathDB

2

Part of 2021 Regional Olympiad of Mexico West

Problems(1)

chain of one or more consecutive digits with product perfect square

Source: Mathematics Regional Olympiad of Mexico West 2021 P2

9/9/2022
Prove that in every 1616-digit number there is a chain of one or more consecutive digits such that the product of those digits is a perfect square.
For example, if the original number is 78623285786327857862328578632785 we can take the digits 66, 22 and 33 whose product is 626^2 (note that these appear consecutively in the number).
number theoryPerfect Square