MathDB

Let

t

be the area of a regular pentagon with each side equal to

1

. Let

P(x)=0

be the polynomial equation with least degree, having integer coefficients, satisfied by

x=t

and the

\gcd

of all the coefficients equal to

1

. If

M

is the sum of the absolute values of the coefficients of

P(x)

, What is the integer closest to

\sqrt{M}

? (

\sin 18^{\circ}=(\sqrt{5}-1)/2

)

Problem Statement