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The Diophantine equation $45x^4-42x^2y^2+5y^4=8$

Here is a practical answer, for the theory or algorithm description check the links, or someone else can elaborate if needed. This is a Thue equation and there are efficient algorithms for finding all ...
Sil's user avatar
  • 16.7k
1 vote

Combinatorial rectangle packing problem

Suppose that $A(n)=m^2$ for some natural numbers $n$ and $m$. That is $$n(n+1)(n+2)(3n+1)=24m^2.$$ This Diophantine equation can be elementarily split into the system of Generalized Pell's equations ...
Alex Ravsky's user avatar
  • 92.3k

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