Suppose n is an integer and consider the number n* – 6n³ – 18n² + 6n + 1. a) By expanding the right-hand side, show that n* – 6n3 – 18n² + 6n + 1 = (n² – 3n – 1)² – 25n². b) Hence find all integersn such that n* – 6n³ – 18n² + 6n + 1 is prime. (regarding negative prime numbers also belong to primes)

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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Suppose n is an integer and consider the number n4−6n3−18n2+6n+1. 

a) By expanding the right-hand side, show that n4−6n3−18n2+6n+1=(n2−3n−1)2−25n2.

b) Hence find all integers n such that n4−6n3−18n2+6n+1 is prime. (regarding negative prime numbers also belong to primes)

Suppose n is an integer and consider the number n* – 6n³ – 18n² + 6n + 1.
a)
By expanding the right-hand side, show that n* – 6n3 – 18n² + 6n + 1 = (n² – 3n – 1)² – 25n².
b)
Hence find all integersn such that n* – 6n³ – 18n² + 6n + 1 is prime. (regarding negative prime
numbers also belong to primes)
Transcribed Image Text:Suppose n is an integer and consider the number n* – 6n³ – 18n² + 6n + 1. a) By expanding the right-hand side, show that n* – 6n3 – 18n² + 6n + 1 = (n² – 3n – 1)² – 25n². b) Hence find all integersn such that n* – 6n³ – 18n² + 6n + 1 is prime. (regarding negative prime numbers also belong to primes)
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