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Tromsø Geophysical Observatory.
Faculty of Science and Technology
UiT, The Arctic University of Norway


TGO Reports no. 3.

A property of repetends of fractions 1/m2n-1 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

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.437-443. 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)m-u, 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.

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