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Omni-MATH / There are F fractions (m)/(n) with the properties: m and n are positive integers with m<n, (m)/(n) is in lowest terms, n is not divisible by the square of any integer larger than 1…

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problem

There are FF fractions mn\frac{m}{n} with the properties: mm and nn are positive integers with m<nm<n, mn\frac{m}{n} is in lowest terms, nn is not divisible by the square of any integer larger than 1, and the shortest sequence of consecutive digits that repeats consecutively and indefinitely in the decimal equivalent of mn\frac{m}{n} has length 6. We define G=F+pG=F+p, where the integer FF has pp digits. What is the sum of the squares of the digits of GG?
Plain-text mathematical notation (without MathML)
There are F fractions (m)/(n) with the properties: m and n are positive integers with m<n, (m)/(n) is in lowest terms, n is not divisible by the square of any integer larger than 1, and the shortest sequence of consecutive digits that repeats consecutively and indefinitely in the decimal equivalent of (m)/(n) has length 6. We define G=F+p, where the integer F has p digits. What is the sum of the squares of the digits of G?
Original LaTeX notation
There are $F$ fractions $\frac{m}{n}$ with the properties: $m$ and $n$ are positive integers with $m<n$, $\frac{m}{n}$ is in lowest terms, $n$ is not divisible by the square of any integer larger than 1, and the shortest sequence of consecutive digits that repeats consecutively and indefinitely in the decimal equivalent of $\frac{m}{n}$ has length 6. We define $G=F+p$, where the integer $F$ has $p$ digits. What is the sum of the squares of the digits of $G$?

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Source and history

task_id
6c14de46-4dd6-50af-b8ac-40a95c8b6a7e
task_key
test--6c14de46-4dd6-50af-b8ac-40a95c8b6a7e
task_revision_id
1
config / split
/ test

Official source

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