Question

find a and b if x^2-x-1 divides ax^5+ bx^4+1​

Answer 1

By really long division i got :-

Q=ax15+(a+b)x14+⋯+(610a+377b)

Q=ax15+(a+b)x14+⋯+(610a+377b)

R=x(987a+610b)+1+610a+377b

R=x(987a+610b)+1+610a+377b

since remainder is 00,

987a+610b=0

987a+610b=0

1+610a+377b=0

1+610a+377b=0

from which i got a=−610,b=987a=−610,b=987

but from wolfram alpha the remainder of −610x17+987x16+1x2−x−1−610x17+987x16+1x2−x−1 is x−1x−1

Thanks.