MathDB

3

Part of 2014 IMAR Test

Problems(1)

Polynomial expressible in a special form !!

Source: IMAR Test 2014 Problem 3

5/14/2015
Let ff be a primitive polynomial with integral coefficients (their highest common factor is 11 ) such that ff is irreducible in Q[X]\mathbb{Q}[X] , and f(X2)f(X^2) is reducible in Q[X]\mathbb{Q}[X] . Show that f=±(u2−Xv2)f= \pm(u^2-Xv^2) for some polynomials uu and vv with integral coefficients.
algebrapolynomialIrreducible