Egyptian Calculation (Decomposition into Unit Fractions of a Binomial)
Author: shiroeExecutions: 370
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Enter the fraction you want to check to see if it can be factored into the sum of two unit fractions.
Enter a natural number between 1 and 100 (inclusive) for the numerator.
Enter a natural number between 1 and 100 (inclusive) for the denominator.
The result will be displayed if a solution is found within the loop limit.
If no solution is found within the loop limit, only the number of loops
will be output. (The fact that no solution is found does not necessarily mean it is algorithmically impossible.
It also includes cases where the range of numbers is too large for manual calculation.)
Enter a natural number between 1 and 100 (inclusive) for the numerator.
Enter a natural number between 1 and 100 (inclusive) for the denominator.
The result will be displayed if a solution is found within the loop limit.
If no solution is found within the loop limit, only the number of loops
will be output. (The fact that no solution is found does not necessarily mean it is algorithmically impossible.
It also includes cases where the range of numbers is too large for manual calculation.)
| Number of loops | (Values of the inverse simplification coefficients leading to the decomposition) |
| Denominator of a unit fraction (1) | The denominator of the first term of a unit fraction expanded into two terms |
| Denominator of a proper fraction (2) | The denominator of the second term in a unit fraction expanded into two terms |
R6 (2024). 08/21 (Wed)_Ver. 003
Displays 50 digits. Fixed-digit display. Real number calculation mode.
Plan: Considering multiple versions, such as factoring into three terms.
Displays 50 digits. Fixed-digit display. Real number calculation mode.
Plan: Considering multiple versions, such as factoring into three terms.
No customer feedback for this calculation yet.
This involves converting a fraction into a sum of unit fractions.
A unit fraction is a fraction whose numerator equals 1.
Both the numerator and denominator of the fraction are natural numbers.
Here, we will consider the case of decomposing a fraction into two unit fractions.
The algorithm used is a reverse simplification loop; this type of algorithm
increases the flexibility of decomposition by repeatedly multiplying the numerator and denominator of the fraction being examined
by the same natural number.This is the reverse of prime factorization—we create composite numbers
to perform the search—but as a way to mimic manual calculation,
simplifying by multiplying by the natural numbers 1, 2, 3, … is a good method.
The results may differ from those of a sequential subtraction algorithm,
since the decomposition of unit fractions does not always yield a unique result.
Since the search range generally has no upper limit, and the numbers involved may become too large
or cause a timeout, we set an upper limit on the number of loop iterations.