# Summed to the Nines: Decimal Expansion of 1/p by Qian Yang '19, Mathematics Colloquium

## Wed, October 10th, 20181:00 pm - 1:45 pm

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Summed to the Nines: Decimal Expansion of 1/p by Qian Yang ’19, Mathematics Colloquium, today 1 – 1:45 pm, Stetson Court Classroom 101.

Abstract:  Consider the decimal expansion of 1/7=0.142857 152857 … If we take the repeating block 142857, split it in half, and add the two halves together, we have 142+857=999. In 1836, Midy proved that for any prime p greater than 5, if the period of the decimal expansion of 1/p is even, then the two halves of the repeating block add up to a string of 9’s. In my colloquium, I am going to prove a theorem recently discovered by Gupta and Sury in 2005, which generalizes Midy’s theorem as follows: given any prime p greater than 5, if we split the period of the decimal expansion of 1/p into an integer number of parts and add these parts together, we will either get a string of 9’s or a multiple of a string of 9’s.