1977 Canadian MO Problems/Problem 4
Problem
Let
![\[p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots +a_1x+a_0\]](http://latex.artofproblemsolving.com/c/1/2/c126ff597ee283022b1c7295806fabde784acccf.png)
and
![\[q(x)=b_mx^m+b_{m-1}x^{m-1}+\cdots +b_1x+b_0\]](http://latex.artofproblemsolving.com/d/f/a/dfabcbca27ad4f78679b62c9b3a5618cc10354f9.png)
be two polynomials with integer coefficients. Suppose that all of the coefficients of the product 
are even, but not all of them are divisible by 4. Show that one of 
and 
has all even coefficients
and the other has at least one odd coefficient.
