Alternating Exponential Prime Finite Sum Polynomial (n=7)

Number Theory Level pending

Let s 7 ( x ) = 7 x 7 + a 6 x 6 + a 5 x 5 7 5 x 4 + 7 4 x 3 7 3 x 2 + 7 2 x 7 s_7(x)=7x^7+a_6x^6+a_5x^5-7^5x^4+7^4x^3-7^3x^2+7^2x-7 . Find a 6 a_6 and a 5 a_5 such that x = 1 7 x=-\frac{1}{7} is a rational root and the sum of the coefficients is 2 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) 2(1+2+3+4+5+6+7) .

( a 6 , a 5 ) = ( 572626 , 512870 ) (a_6,a_5)=(572626,-512870) ( a 6 , a 5 ) = ( 527626 , 518270 ) (a_6,a_5)=(527626,-518270) ( a 6 , a 5 ) = ( 527626 , 512870 ) (a_6,a_5)=(527626,-512870) ( a 6 , a 5 ) = ( 527626 , 512870 ) (a_6,a_5)=(-527626,512870)

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1 solution

Frank Giordano
May 12, 2017

if you know anyone workin on the Reimann Hypothesis, send them here please: https://www.facebook.com/groups/factorthis/

Frank Giordano - 4 years ago

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