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infinite naturals in form k^2 + 1 without any real divisors of same form

Source: 11th QEDMO p12 Seniors (6-8. 12. 2012) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 16, 2021
number theoryDivisorsdividesdivisible

Problem Statement

Prove that there are infinitely many different natural numbers of the form k2+1k^2 + 1, kāˆˆNk \in N that have no real divisor of this form.
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