On the periods of generalized Fibonacci recurrences
On the periods of generalized Fibonacci recurrences
We give a simple condition for a linear recurrence <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis mod 2 Superscript w Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mspace width="0.667em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi>mod</mml:mi> <mml:mspace width="0.333em" /> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>w</mml:mi> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\pmod {2^w}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of degree <italic>r</italic> to have the …