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perfect squares after multiplying 2-digit numbers with 588

Source: 2019 Dürer Math Competition Finals Day2 E2 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
Perfect Squarenumber theory

Problem Statement

Anne multiplies each two-digit number by 588588 in turn, and writes down the so-obtained products. How many perfect squares does she write down?