Using the solutions of the Pell equation:

Solutions have the form:

]]>http://www.mathunion.org/general/prizes/2014/

As not fair. He no single formula did not write and say it is good work.

I wrote so many formulas and are not allowed to publish.

http://www.mathunion.org/general/prizes/2014/

His work there.

http://arxiv.org/pdf/1006.1002v2.pdf

http://arxiv.org/pdf/1007.0052v1.pdf

Funny. He can't solve a single equation. Can't write a single formula.

Even says on the contrary that the formulas cannot be obtained.

But it's not. In some cases, to obtain a formula for the solution.

They strongly opposed the formulas.

]]>http://www.artofproblemsolving.com/Foru … 6&t=602478

You can compare solutions.

]]>This is equivalent to solving the following system of equations:

Let:

- any asked us integers.For ease of calculation, let's make a replacement.

Then the solutions are of the form:

]]>Then the solutions are.

]]>Solutions have the form:

An interesting case when:

For this we need to solve the Pell equation:And solutions to substitute in the formula.

]]>Solutions are provided by the Pell equation.

And have a look.

Solving the Pell equation can be found. Knowing the past can be found .

You can start with.

All numbers can have any sign.

Another can be reduced to 4. And come to the equation. ]]>

If the ratio is the square.

Using the solutions of the equation Pell.

Then the solutions are.

]]>You can write a simple solution:

- any integer asked us.]]>Then this equation. If there is a solution - they are infinitely many.

Finding solutions-it factor. To factor.

We use the solutions of the equation Pell.

Then the solutions are.

]]>The solutions have the form:

................................................

..............................................

Will make a replacement.

The solution has the form:

]]>Fermat's theorem cannot be proved, if you do not know how to solve Diophantine equations.

This approach cannot be used. This equation has a solution.

The solutions have the form:

- any integer.]]>