If we do the replacement.

Then the solution will have the form:

]]>Equivalent to the need to solve the following system of equations.

To ease calculations we change.

Then we need the number to obtain Pythagorean triples can be found by the formula.

At any stage of the computation can be divided into common divisor.

]]>We must remember that then can be reduced by a common factor.

]]>http://math.stackexchange.com/questions … 363#831363

So writes the Pell equation in General form.

If we know any solution of this equation.

If we use any solutions of the following equation Pell.

Then the following solution of the desired equation can be found by the formula.

]]>http://math.stackexchange.com/questions … e-patterns

If we consider the equation of a certain type.

The solutions can be written simply using the sequence. The next element which is obtained from the previous one.

If we use the first element of the sequence.

Then the formula will look like.

If we use the first element of the sequence.

Then the formula will look like.

]]>This is solvable if and only if gcd(*a*,*b*) divides *c*. The general solution is

where

and *X*=*x*, *Y*=*y* is a particular solution. See this post:

Decisions are not always there. To find out, I use too much. Decompose the multiplier number.

Finding the number $t$ and $k$, the solution writes:

]]>Has this type:

One easy solution can be written as:

- integers which we ask.It is better to write such a decision.

- any integer.]]>If you can imagine.

Then decisions can be recorded.

If you can imagine.

Then decisions can be recorded.

- integers which we ask.]]>If you can decompose the coefficient multipliers as follows:

Their work squares:

Then decisions can be recorded.

You can add another simple option. If the ratio can be written as:

Then decisions can be recorded.

]]>When the standard approach solution and using a replacement.

Then the solution can be written as :

- integers which we ask.]]>If you can represent numbers as:

This decision when the coefficients are related through the equation of Pell.

To simplify calculations we will make this change.

Then the solution can be written:

- integers which we ask.]]>If the number

is the problem any, and is such as this:Then the solution can be written:

- integers which we are set.It's my decision.

How did you solve the other you can see there.

http://mathoverflow.net/questions/38354 … 180#196180

write the formula so that it was easier to go through. To facilitate calculations will make the replacement.

Then decisions can be recorded and they are.

- integers, which we ask.]]>