Can Diophantine Equations Determine When an Equation is Prime?

  • Thread starter ~Death~
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In summary, the conversation revolved around the topic of writing an article for an undergraduate math journal. The speaker mentioned being jealous of a friend who had previously done so and was wondering if their Python program that finds and counts solutions to a diophantine equation could be enough to write about. They also expressed concern about being laughed at and the importance of ensuring the correctness of their results before submitting. The conversation ended with the speaker acknowledging that they may be getting ahead of themselves and seeking other ideas for potential topics.
  • #1
~Death~
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I've always wanted to write an article for an undergrad math journal- i had a friend who did it

and I am kind of jealous lol

ive programmed in python a simple program that finds and counts the solutions to a diophantine equation

and I'm wondering if I found the set of solutions that determines when an equation

f(x,y) is prime

would that be enough to write something?

Or would i just get laughed at ?
 
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  • #2
I would be very careful that the result is correct before sending it in.
 
  • #3
ok thanks

itd definitely take me awhile and id make sure it was correct

maybe if anyone has other ideas on what i could try and write on

i mean i only just finished 2nd year so maybe I am getting a bit ahead of myself
 
  • #4
There are a number of sets of diophantine equations where all solutions define prime numbers and all prime numbers have corresponding solutions, but afaik no one has found a solution for even one of these sets. good luck
 

FAQ: Can Diophantine Equations Determine When an Equation is Prime?

1. What is a Diophantine Equation?

A Diophantine Equation is a polynomial equation in two or more variables where the coefficients and solutions are restricted to be integers. It is named after the ancient Greek mathematician Diophantus.

2. What is the significance of Diophantine Equations?

Diophantine Equations are important in number theory and have applications in cryptography, coding theory, and other areas of mathematics and computer science.

3. How do you solve a Diophantine Equation?

Solving a Diophantine Equation involves finding integer solutions that satisfy the equation. Various techniques can be used, including factorization, substitution, and modular arithmetic.

4. What is the difference between a Diophantine Equation and a linear equation?

A Diophantine Equation can have multiple variables and involves finding integer solutions, while a linear equation only has one variable and can have non-integer solutions.

5. Can all Diophantine Equations be solved?

No, not all Diophantine Equations have integer solutions. Some have no solutions at all, while others may have infinitely many solutions.

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