Recent content by individ

Leave the rest of modular arithmetic. Should equation to solve. You generally solutions not, and they are when the number is negative. I asked about the decision not such equation, and such? $$aXY-X-Y=Z^2$$

Not the correct solution. The condition for which solutions need to come from the solution, not the solution of the conditions that we want to impose. Very often many so decide. Your mistake is easily detected if you need to find a solution to the equation: $$aXY-X-Y=Z^2$$ How do You then the...

And what answer do not like? The formula is. What problems?

You can write and easy solution and similar equation: number theory - Find all integers satisfying $m^2=n_1^2+n_1n_2+n_2^2$ - Mathematics Stack Exchange There are many formulas to see. The questions will be answered here.

For example for such equation: $$y^2+ax^2=z^2$$ The solutions have the form: $$y=p^2-as^2$$ $$x=2ps$$ $$z=p^2+as^2$$ For example for such equation: $$y^2+ax^2=az^2$$ The solutions have the form: $$y=2aps$$ $$x=ap^2-s^2$$ $$z=ap^2+s^2$$ $$p,s$$ - integers. But for such equations...

Thank you! When you need an answer I will give a link to it.

Once you know how to solve it, then explain how to solve Diophantine equation: $$X^2+Y^2=aZ^2$$ $$a$$ - integer. Write the equation when it has a solution.

I don't understand. Why such a simple equation so long to decide? The solution was recorded immediately!

Equation: $$18x+5y=48$$ Has the solution: $$x=5k+1$$ $$y=6-18k$$ equation: $$158x-57y=7$$ Decisions no.

In the equation: $$X^2+Y^2=qZ^3$$ If the ratio is such that the root of an integer: $$c=\sqrt{q-1}$$ Then the solution is: $$X=-2(c+1)p^6+4(2c(q-2)-3q)p^5s+2(c(5q^2-2q-8)-q^2-22q+8)p^4s^2+$$$$8q(5q^2-14q+4)p^3s^3+$$...

Generally always better to record the formula itself. Especially when she looks rather cumbersome. For example, even for a particular case, it is not simple. the equation: $$X^2+Y^2=Z^3$$ Has the solutions...

The problem is that when I got the formula that led below - there was a question whether they really describe all the decisions? But has not yet found a counterexample, and it exists at all interested or not? Although the discussion of this issue in many other forums and did not work. Everyone...