Jordannmoore4276 Jordannmoore4276
  • 03-07-2020
  • Mathematics
contestada

Prove that for all n E N\{0}, n3 + 2n and n4 +3n2 +1 are relatively prime.

Respuesta :

Newton9022 Newton9022
  • 05-07-2020

Answer:

Two expressions are relatively prime if their greatest common divisor is one.

Given the terms: [tex]n^3 + 2n$ and n^4 +3n^2 +1[/tex], [tex]n \in N|\{0\}}[/tex]

[tex]n^3 + 2n=n(n^2+2)\\n^4 +3n^2 +1$ is not factorizable\\[/tex]

Therefore, the greatest common divisor of the two expressions is 1.

Therefore, for all n in the set of natural numbers, (where n cannot be zero.) The two expressions are relatively prime.

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