5

Part of 2009 ISI B.Math Entrance Exam

Problems(1)

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

Source:

p

be a prime number bigger than

5

. Suppose, the decimal expansion of

\frac{1}{p}

0.\overline{a_1a_2\cdots a_r}

where the line denotes a recurring decimal. Prove that

10^r

leaves a remainder of

1

p

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