- MNT 12.1
- MNT 12.2 You may compute the discriminant with respect to the basis .
- MNT 12.4. In this problem “integer” means algebraic integer, the conjugate of means . Also, is the absolute value of (viewed as a complex number). Hint: can you bound the number of quadratic monic polynomials with integer coefficients?
- MNT 12.6
- MNT 12.9. You may work this for an irreducible cubic rather than a reducible cubic, if you prefer, using 12.1.4.

Advertisements
(function(){var c=function(){var a=document.getElementById("crt-944397698");window.Criteo?(a.parentNode.style.setProperty("display","inline-block","important"),a.style.setProperty("display","block","important"),window.Criteo.DisplayAcceptableAdIfAdblocked({zoneid:388248,containerid:"crt-944397698",collapseContainerIfNotAdblocked:!0,callifnotadblocked:function(){a.style.setProperty("display","none","important");a.style.setProperty("visbility","hidden","important")}})):(a.style.setProperty("display","none","important"),a.style.setProperty("visibility","hidden","important"))};if(window.Criteo)c();else{if(!__ATA.criteo.script){var b=document.createElement("script");b.src="//static.criteo.net/js/ld/publishertag.js";b.onload=function(){for(var a=0;a<__ATA.criteo.cmd.length;a++){var b=__ATA.criteo.cmd[a];"function"===typeof b&&b()}};(document.head||document.getElementsByTagName("head")[0]).appendChild(b);__ATA.criteo.script=b}__ATA.criteo.cmd.push(c)}})();
(function(){var c=function(){var a=document.getElementById("crt-1018678988");window.Criteo?(a.parentNode.style.setProperty("display","inline-block","important"),a.style.setProperty("display","block","important"),window.Criteo.DisplayAcceptableAdIfAdblocked({zoneid:837497,containerid:"crt-1018678988",collapseContainerIfNotAdblocked:!0,callifnotadblocked:function(){a.style.setProperty("display","none","important");a.style.setProperty("visbility","hidden","important")}})):(a.style.setProperty("display","none","important"),a.style.setProperty("visibility","hidden","important"))};if(window.Criteo)c();else{if(!__ATA.criteo.script){var b=document.createElement("script");b.src="//static.criteo.net/js/ld/publishertag.js";b.onload=function(){for(var a=0;a<__ATA.criteo.cmd.length;a++){var b=__ATA.criteo.cmd[a];"function"===typeof b&&b()}};(document.head||document.getElementsByTagName("head")[0]).appendChild(b);__ATA.criteo.script=b}__ATA.criteo.cmd.push(c)}})();