MathDB

Let

p > 3

be a prime number. A sequence of

p-1

integers

a_1,a_2, \dots, a_{p-1}

is called wonky if they are distinct modulo

p

and

a_ia_{i+2} \not\equiv a_{i+1}^2 \pmod p

for all

i \in \{1, 2, \dots, p-1\}

, where

a_p = a_1

and

a_{p+1} = a_2

. Does there always exist a wonky sequence such that

a_1a_2, \qquad a_1a_2+a_2a_3, \qquad \dots, \qquad a_1a_2+\cdots +a_{p-1}a_1,

are all distinct modulo

p

?
Proposed by Harun Khan

Problem Statement