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B.Math(Hons.) Admission Test 2009 problem 5

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April 9, 2012
number theory unsolvednumber theory

Problem Statement

Let pp be a prime number bigger than 55. Suppose, the decimal expansion of 1p\frac{1}{p} looks like 0.a1a2⋯ar‾0.\overline{a_1a_2\cdots a_r} where the line denotes a recurring decimal. Prove that 10r10^r leaves a remainder of 11 on dividing by pp.
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