box% sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 8.8, Release Date: 2019-06-26                     │
│ Using Python 2.7.16. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
sage: R.<x,y,z,s>=PolynomialRing(QQ, order='lex')
sage: ideal(x^2 - 2, y^2 - 3, z^2 - 5, s - (x + y + z)).groebner_basis()[-1]
s^8 - 40*s^6 + 352*s^4 - 960*s^2 + 576
sage: p = _
sage: factor(576)
2^6 * 3^2
sage: any(p(s=sign*2^i*3^j) == 0  for sign in (1, -1) for i in range(6+1) for j in range(2+1))
False