Is this number a composite?

Algebra Level 2

Is the number 16 x 8 + 32 x 6 y + 24 x 4 y 2 + 4 x 4 + 8 x 2 y 3 + y 4 16 x^8 + 32 x^6 y + 24 x^4 y^2 + 4 x^4 + 8 x^2 y^3 + y^4 composite?

Cannot be determined No Yes

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1 solution

Tomáš Hauser
Jan 19, 2020

16 x 8 + 32 x 6 y + 24 x 4 y 2 + 4 x 4 + 8 x 2 y 3 + y 4 = ( 16 x 8 + 32 x 6 y + 24 x 4 y 2 + 8 x 2 y 3 + y 4 ) + 4 x 4 = 16 x^8 + 32 x^6 y + 24 x^4 y^2 + 4 x^4 + 8 x^2 y^3 + y^4 = (16 x^8 + 32 x^6 y + 24 x^4 y^2 + 8 x^2 y^3 + y^4) + 4x^4 =

= ( 2 x 2 + y 4 ) 4 + 4 x 4 = ( ( 2 x 2 + y ) 2 + 2 ( 2 x 2 + y ) x + 2 x 2 ) ( ( 2 x 2 + y ) 2 2 ( 2 x 2 + y ) x + 2 x 2 ) =(2x^2 + y^4)^4 + 4x^4 = ((2 x^2 + y)^2 + 2 (2 x^2 + y) x + 2 x^2) ((2 x^2 + y)^2 - 2 (2 x^2 + y) x + 2 x^2)

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