Let p≥7 be a prime number, ζ a primitive pth 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 pth cyclotomic field.)
K. Gyory superior algebrasuperior algebra unsolved