Here is another typical example. This proves that fights with me. Because of the method of solution.
Integer polynomials taking square valuesInteger polynomials taking square values
Ask for exactly the formula for solving the equation. I wrote a formula linking this equation with equation Pell. I wrote the formula in General. You can substitute any of the coefficients. These formulas look quite simple.
For these equations we use the standard approach.
For a private quadratic form: $$Y^2=aX^2+bX+1$$
Using solutions of Pell's equation: $$p^2-as^2=1$$
Solutions can be expressed through them is quite simple.
$$Y=p^2+bps+as^2$$ $$X=2ps+bs^2$$
$p,s$ - these numbers can have any sign. Finding solutions of equations Pell - standard procedure.
Most interesting is that all the examples which lead shows the relationship of this equation with Equation Pell. What is the point to write thousands of sequences ? If there's one formula that describes them all.
Bring as an example the numbers, and it is good. When I write a formula - it require to remove!
