MathDB

Let

p\geq 7

be a prime number,

\zeta

a primitive

p

th root of unity,

c

a rational number. Prove that in the additive group generated by the numbers 1,\zeta,\zeta^2,\zeta^3\plus{}\zeta^{\minus{}3} there are only finitely many elements whose norm is equal to

c

. (The norm is in the

p

th cyclotomic field.) K. Gyory

Problem Statement