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Unformatted text preview: March 17, 2005 Physics 681481; CS 483: Assignment #5 (please hand in after the lecture, Thursday, April 7th, in three weeks) The two questions that follow illustrate the mathematics of the final (postquantum computational) stage of Shors period finding procedure, as described on pages 16 and 17 of Chapter 3 of the lecture notes. The detective work you are asked to carry out makes use of the theorem, cited in the lecture notes, that if j and r have no common factors, and x is an estimate for the fraction j/r that differs from it by less than 1 / 2 r 2 , then j/r will appear as one of the partial sums in the continued fraction expansion of x . 1. Suppose you know that the integer r is less than 100 and that 11883 is within 1 2 of an integral multiple of 2 14 /r . What is r ? 2. Suppose you know that the integer r is less than 100 and that 11703 and 15019 are both within 1 2 of integral multiples of 2 14 /r . What is r ?...
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 Spring '05
 ANON
 Physics

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