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4n + 1 and 9n + 1 are perfect squares

Source: 9th QEDMO p1 Juniors (21-22. 9. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 15, 2021

number theoryPerfect Square

Problem Statement

Find all integers

n

for which both

4n + 1

and

9n + 1

are perfect squares.