show that 8^n + 1 is a composite number
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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.
(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.
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