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3x+1 and 6x-2 are perfect squares while 6x^2 -1 is prime

Source: Tuymaada Junior 2003 p2

May 11, 2019

number theoryprimePerfect SquaresPerfect Square

Problem Statement

Find all natural

x

for which

3x+1

and

6x-2

are perfect squares, and the number

6x^2-1

is prime.