) Write ‘There are infinitely many natural numbers n, such that 5n2 + 1 is a square number’ as a formal quantified statement. [Hint: You can express ‘infinitely many’ as ‘arbitrarily large’.]

) Write ‘There are infinitely many natural numbers n, such that 5n2 + 1 is a square number’ as a formal quantified statement. [Hint: You can express ‘infinitely many’ as ‘arbitrarily large’.]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

: (a) Write ‘There are infinitely many natural numbers n,
such that 5n² + 1 is a square number’ as a formal quantified statement.
[Hint: You can express ‘infinitely many’ as ‘arbitrarily large’.]
(b) Prove or disprove the statement
∀n ∈ N: ln(n + 1) ≤ 1 +1/2+ · · · +1/n≤ 1 + ln(n)

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