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### Classification of the positive integers not being the sum of four non-zero squares

It is well known that every positive integer is the sum of at most four perfect squares (including $1$). But which positive integers are not the sum of four non-zero perfect squares ($1$ is still ...
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### Maps of primitive vectors and Conway's river, has anyone built this in SAGE?

I am attempting to teach number theory from John Stillwell's Elements of Number Theory in the upcoming semester. There are two sections (5.7 and 5.8) which describe the diagrammatic method for the ...
### Find all integer solutions for the equation $|5x^2 - y^2| = 4$
In a paper that I wrote as an undergraduate student, I conjectured that the only integer solutions to the equation $$|5x^2 - y^2| = 4$$ occur when $x$ is a Fibonacci number and $y$ is a Lucas number. ...