jats:pWhat values of the Standard Model hypercharges result in a mathematically consistent quantum field theory? We show that the constraints imposed by the lack of gauge anomalies can be recast as the equation jats:inline-formulajats:alternativesjats:tex-mathx^3 + y^3 = z^3</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">mml:mrowmml:msupmml:mix</mml:mi>mml:mn3</mml:mn></mml:msup>mml:mo+</mml:mo>mml:msupmml:miy</mml:mi>mml:mn3</mml:mn></mml:msup>mml:mo=</mml:mo>mml:msupmml:miz</mml:mi>mml:mn3</mml:mn></mml:msup></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>. If hypercharge is quantised, then jats:inline-formulajats:alternativesjats:tex-mathx</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">mml:mix</mml:mi></mml:math></jats:alternatives></jats:inline-formula>, jats:inline-formulajats:alternativesjats:tex-mathy</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">mml:miy</mml:mi></mml:math></jats:alternatives></jats:inline-formula> and jats:inline-formulajats:alternativesjats:tex-mathz</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">mml:miz</mml:mi></mml:math></jats:alternatives></jats:inline-formula> must be integers. The trivial (and only) solutions, with jats:inline-formulajats:alternativesjats:tex-mathx=0</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">mml:mrowmml:mix</mml:mi>mml:mo=</mml:mo>mml:mn0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> or jats:inline-formulajats:alternativesjats:tex-mathy=0</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">mml:mrowmml:miy</mml:mi>mml:mo=</mml:mo>mml:mn0</mml:mn></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, reproduce the hypercharge assignments seen in Nature. This argument does not rely on the mixed gauge-gravitational anomaly, which is automatically vanishing if hypercharge is quantised and the gauge anomalies vanish.</jats:p>