TGO Reports no. 3.
A property of repetends of fractions 1/m^{2n1} with m prime, equal to 3 modulus 4, and n any positive integer
O.J. Rødseth, S. Wennevold, N.J. Armstrong and R.J.Armstrong
Abstract:
Consider the length of the repeating part (period length) of the digital expansion of 1/m as in Table 1 of
Math.Gaz. 87 (November 2003) pp.437443. When m is prime, and has the form 4t+3, with t a positive integer,
we consider the sequence of period lengths as a function of base.
We prove that for individual bases xm +u and (x+1)mu,
u<m, the period lengths are a factor 2 different. Here again x and u are positive integers. We show that the same result holds for any odd power of m.
Full text (384 KB .pdf)
