Diophantine Equation Ppt -
Slide 1: Title Slide
Title: Diophantine Equations: Theory and Applications
Subtitle: Solving Integer Equations from Ancient Greece to Modern Number Theory
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: Focuses on "forming" and "manipulating" equations, specifically using factorisation tools like the difference of two squares [27]. McGill University Colloquium Slides diophantine equation ppt
Slide 11: Real-World Applications
- Cryptography: RSA and elliptic curve cryptography rely on integer equations.
- Coding Theory: Error-correcting codes (Goppa codes, AG codes).
- Chemistry: Balancing chemical equations = linear Diophantine.
- Computer Science: Integer programming (NP-hard subset).
- Physics: Quantization conditions in string theory (e.g., ( p^2 + q^2 = N )).
- Title: Solutions to Diophantine Equations
- Bullet points:
Conclusion & Further Reading: Summarizes main points and suggests references (e.g., Number Theory by Niven, Zuckerman, Montgomery). Slide 1: Title Slide Title: Diophantine Equations: Theory
Slide 14: Thank You & Questions
- Further reading:
“Number Theory” by Niven/Zuckerman/Montgomery
“Unsolved Problems in Number Theory” by Guy
“Diophantine Equations” by Mordell - Tools: SageMath, Mathematica, PARI/GP for computational solving.
These resources provide a structured narrative, from basic definitions to advanced number theory concepts: Cryptography: RSA and elliptic curve cryptography rely on
- Further reading:
- Computational Search (for small bounds):
