Question

divide n^3-3n^2+5n-3 by n^2-2

Answer 1

Answer:

If 3 is a multiple of n then3|n3+3n2+5n+3

Let gcd (n , 3) = 1. Then by Fermat’s little theorem

n2≡1(mod3)

⟹n3≡n(mod3)

⟹n3≡n−6n(mod3)

⟹n3≡−5n(mod3)

⟹n3+5n≡0(mod3)

⟹n3+3n2+5n+3≡0(mod3)

∴3|n3+3n2+5n+3