MHB 57^(th) digit in decimal expansion

AI Thread Summary
The discussion focuses on calculating the 57th digit in the decimal expansion of 1/57. It highlights the use of modular arithmetic and Euler's phi function to determine the period of the decimal expansion. By finding the period, one can compute earlier digits in the sequence, simplifying the process. The approach emphasizes efficiency in calculating specific digits without needing to compute the entire decimal expansion. Understanding these mathematical tools is crucial for accurately determining the desired digit.
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Calculation of $57^{th}$ digit in the decimal expansion of $\displaystyle \frac{1}{57}$
 
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jacks said:
Calculation of $57^{th}$ digit in the decimal expansion of $\displaystyle \frac{1}{57}$

If you are allowed mod calculation and Euler's phi function, you can use >>this<<.
It gives you the period of the decimal expansion, meaning it suffices to calculate a decimal that comes much earlier in the expansion.
 
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