MathDB

Say a real number

r

is \emph{repetitive} if there exist two distinct complex numbers

z_1,z_2

with

|z_1|=|z_2|=1

and

\{z_1,z_2\}\neq\{-i,i\}

such that

z_1(z_1^3+z_1^2+rz_1+1)=z_2(z_2^3+z_2^2+rz_2+1).

There exist real numbers

a,b

such that a real number

r

is \emph{repetitive} if and only if

a < r\le b

. If the value of

|a|+|b|

can be expressed in the form

\frac{p}{q}

for relatively prime positive integers

p

and

q

, find

100p+q

.
Proposed by James Lin

Problem Statement