MathDB

2

Part of 2015 India National Olympiad

Problems(1)

Inmo 2015

Source: inmo 2015 #2

2/1/2015
For any natural number n>1n > 1 write the finite decimal expansion of 1n\frac{1}{n} (for example we write 12=0.49‾\frac{1}{2}=0.4\overline{9} as its infinite decimal expansion not 0.5)0.5). Determine the length of non-periodic part of the (infinite) decimal expansion of 1n\frac{1}{n}.
inductionnumber theory unsolvednumber theory