Math Problem Statement
When expanded as a decimal, the fraction $\frac{1}{977}$ has a repetend (the repeating part of the decimal) that begins right after the decimal point, and is $976$ digits long. If the last three digits of the repetend are $ABC$, compute the digits $A$, $B$, and $C$.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Number Theory
Modular Arithmetic
Repeating Decimals
Formulas
a^{p-1} \equiv 1 \mod p (Fermat's Little Theorem)
Theorems
Fermat's Little Theorem
Properties of Repeating Decimals
Suitable Grade Level
Advanced High School, Grades 11-12
Related Recommendation
Compute Last Three Digits of Repetend for 1/977
Find Digit A in the Repeating Decimal of 1/97 with A67 as the Last Three Digits
Find the Last Two Digits of 9^2019 using Modular Arithmetic
Find the Digit at 1/10^70 in the Repeating Decimal 0.2019...
Remainder of Sum of Powers Modulo 10100 - Detailed Solution