Research:Algorithm to determine if two numbers are coprime

Contact

Pedro Hugo García Peláez hugo117711@gmail.com

This page documents a completed research project.

Methods

1. Take two input numbers, let's call them num1 and num2.

2. Calculate the Pochhammer symbol or rising factorial using the following formula: pochhammer = (num1/num2) * ((num1/num2) + 1)

3. Check if the pochhammer is divisible by both num1 and num2 without any remainder. If it is, then the numbers are coprime. Otherwise, they are not coprime.

4. To check for divisibility, calculate the remainder when pochhammer is divided by num1 and num2 separately. remainder1 = numerator of pochhammer % num1 remainder2 = denominator pochhammer % num2

5. If either remainder1 or remainder2 is not equal to zero, then the numbers are not coprime. Otherwise, they are coprime.

Here's a translation of the given example: (127/27) * ((127/27) + 1) = 19558/729 19558/127 = 154 (no remainder) 729/27 = 27 (no remainder) Therefore, both numbers are coprime. (889/189) * ((889/189) + 1) = 19558/729 19558/889 = 22 (no remainder) 729/189 = 3.85... (remainder exists) Therefore, the numbers are not coprime.

Timeline

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