The British Mathematical Olympiad Diophantine Equation
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- Опубліковано 18 чер 2024
- The British Mathematical Olympiad Diophantine Equation
Join us as we delve into the intricate world of Diophantine equations with a challenge straight from the British Mathematical Olympiad! In this video, we explore the elegance and complexity of solving Diophantine equations, a cornerstone of algebraic problem-solving. Get ready to sharpen your mathematical skills and embark on a journey of discovery with this captivating BMO challenge!
Topics Covered:
1. Understanding the basics of radical Diophantine equation in integers
2. Analyzing the unique properties and substitution of the given equation.
3. Step-by-step approach to solving the BMO Challenge for positive integers.
4. Tips and tricks for handling three variable Diophantine equation like a pro.
5. Algebraic identities and manipulations while solving equations.
Timestamps:
0:00 Introduction
1:14 Algebraic identities
3:41 Algebraic manipulations
4:45 Prime factorization
8:45 Positive integers
11:25 All positive triples
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Thanks for Watching!
@infyGyan
A wonderful explanation...smartness think 🤔..thanks
from equation 1, z = x + y - 12, substituting this to equation 2
x^2 + y^2 - (x + y - 12)^2 = -2xy + 24x + 24y - 144 = 12
which gives xy -12x -12y + 78 =0 and (x - 12) * (y - 12) = 66
Wow! who would think of +66 to both sides in the middle of process. Good Job! ^.^
I tried sir.I did not get any idea.Thank you.
Keep watching.
thanks
@@infyGyan thank you.