This article begins with an introduction to a conjecture made around 1930 in the
area of Diophantine approximation: the Littlewood Conjecture. The conjecture asks
whether any two real numbers can be simultaneously well approximated by rational
numbers with the same denominator. The introduction also focuses briefly on an
analogue of this conjecture, regarding power series and polynomials with coefficients
in an infinite field. Harold Davenport and Donald Lewis disproved this analogue
of the Littlewood Conjecture in 1963. Following the introduction we focus
on a claim relating to another analogue of this conjecture. In 1970, John
Armitage believed that he had disproved an analogue of the Littlewood
Conjecture, regarding power series and polynomials with coefficients in a
finite field. The remainder of this article shows that Armitage’s claim was
false.
