Alf van der Poorten CeNTRe for Number Theory Research (Australia)
An awful problem about integers in base four Back in the early eighties, John Loxton and I had our attention
captured by a question of Brown and Moran concerning a construction seemingly relevant to work that
eventually led to their 1984 paper with Tijdeman: “Riesz products are basic measures”. In brief, one may of
course write the integers in base four using 0, �1, and 2 as the four digits. Can every integer be
expressed as a quotient of integers requiring just the three digits 0, and �1? Such questions are
notoriously slippery and John and I therefore remain inordinately proud of the clever tricks we
eventually recalled, after far too much effort, to settle the issue. I will tell the story of our travails.
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