( x 5 + x 4 + 1 ) (x^5 + x^4 + 1) cannot be a prime?

Number Theory Level 3

True or False?

\quad If f ( x ) = x 5 + x 4 + 1 f(x) = x^5 + x^4 + 1 , then f ( x ) f(x) can never be a prime for integer x > 1 x > 1 .

True False

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Ossama Ismail
Jan 24, 2017

Answer is True :

( x 5 + x 4 + 1 ) = ( x 3 − x + 1 ) ( x 2 + x + 1 ) (x^5 + x^4 + 1) = ( x^3 - x +1)(x^2 +x+1)

for x > 1 x > 1

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