Скачать или смотреть The Impossible Equation: Why 5x² − 4y² = 7 Has No Integer Solutions

Unlock the secret behind the Diophantine equation 5x² − 4y² = 7, a deceptively simple expression with no integer solutions!
In this short deep-dive, we walk through the number-theoretic reasoning that proves the equation is mathematically impossible to satisfy.
We explore:
Why equations of this form usually do have solutions
How modular arithmetic exposes contradictions
The structure behind Pell-type equations
What makes this one different
If you enjoy math mysteries, Diophantine equations, or elegant number-theory proofs, you’ll love this one.
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Diophantine equations
number theory
impossible equation
math proof
integer solutions
unsolved problems
5x2 - 4y2 = 7
Pell equation
no integer solutions
modular arithmetic
math tutorial
algebra problem
math mystery

0:00 Introduction and statement of the problem
0:11 We reduce the equation mod 4
0:48 Our reduced equation
1:08 The quadratic least residues mod 4
1:19 We arrive at our contradiction