Question

show that 8^n + 1 is a composite number

Answer 1

Hi there,


(8^n) + 1 , here n should be a whole number, as given that it's an integer

= {(2^3)}^n + 1

Or, {(2^n)^3} + 1 , which is in the form of

a^3 + b^3.

that means a^3 + b^3 has two factors

i.e. (a+b)(a^2+ab+b^2)

which has two factors [other than 1 and itself].

Hence, 8^n + 1

=2^n^3 + 1^3

=(2^n + 1)(2^n^2 + 2^n + 1)

>>>PROVED///


#SB.