The equation x^n + y^n = z^n is true for some positive rational numbers n, x, y and z if, and only if, there is some angle, say r, such that for every triangle that has one longest side and that has the angle r as the angle which is opposite to its longest side, say c, the equation a^n + b^n = c^n, where a and b are the lengths of its other two sides, is true. In the case where n = 2, r = 90 degrees.
The following is the continuation of my comment below:
3- For every three positive rational numbers x, y and z, if x + y is not equal to z, z is greater than both x and y, and x, y, and z are not the lengths of the sides of a right triangle, then there is a positive irrational number n such that x^n + y^n = z^n.
If 1-, 2- and 3- are true, then the set of irrational numbers is countable.
1- If n is a positive irrational number, then the equation x^n + y^n = z^n has solutions in positive rational numbers x, y and z.
2- If a positive number n is different from 0, 1 and 2, then if (x1, y1, z1) and (x2, y2, z2) are any two solutions of the equation x^n + y^n = z^n such that x1, y1, z1, x2, y2 and z2 are all positive numbers, then x1/y1 = x2/y2, x1/z1 = x2/z2 and y1/z1 = y2/z2.
The following is the continuation of my comment below:
3- For every three nonzero rational numbers x, y and z, if x + y is not equal to z, z is greater than both x and y, and x, y, and z are not the lengths of the sides of a right triangle, then there is a nonzero irrational number n such that x^n + y^n = z^n.
If 1-, 2- and 3- are true, then the set of irrational numbers is countable.
1- If n is a nonzero irrational number, then the equation x^n + y^n = z^n has solutions in nonzero rational numbers x, y and z.
2- If a number n is different from 0, 1,-1, 2, and -2 , then if (x1, y1, z1) and (x2, y2, z2) are any two solutions of the equation x^n + y^n = z^n such that x1, y1, z1, x2, y2 and z2 are nonzero numbers, then x1/y1 = x2/y2, x1/z1 = x2/z2 and y1/z1 = y2/z2.
Es que este video esta extraido del documental y solo es una parte que necesitaba para una presentacion en una de las asignaturas de la carrera. Pero en youtube tienes el video completo.
me dejo flipado
fidel11rodriguez 1 year ago
To know about the new Fermat's proof, click on the left.
Watch video and read the entire description.
fermatxxi 1 year ago
If n is a real number greater than 1 and x^n + y^n = z^n, then x, y and z must be the lengths of the sides of some triangle.
jahdallah 3 years ago
The equation x^n + y^n = z^n is true for some positive rational numbers n, x, y and z if, and only if, there is some angle, say r, such that for every triangle that has one longest side and that has the angle r as the angle which is opposite to its longest side, say c, the equation a^n + b^n = c^n, where a and b are the lengths of its other two sides, is true. In the case where n = 2, r = 90 degrees.
jahdallah 3 years ago
The following is the continuation of my comment below:
3- For every three positive rational numbers x, y and z, if x + y is not equal to z, z is greater than both x and y, and x, y, and z are not the lengths of the sides of a right triangle, then there is a positive irrational number n such that x^n + y^n = z^n.
If 1-, 2- and 3- are true, then the set of irrational numbers is countable.
jahdallah 3 years ago
1- If n is a positive irrational number, then the equation x^n + y^n = z^n has solutions in positive rational numbers x, y and z.
2- If a positive number n is different from 0, 1 and 2, then if (x1, y1, z1) and (x2, y2, z2) are any two solutions of the equation x^n + y^n = z^n such that x1, y1, z1, x2, y2 and z2 are all positive numbers, then x1/y1 = x2/y2, x1/z1 = x2/z2 and y1/z1 = y2/z2.
jahdallah 3 years ago
The following is the continuation of my comment below:
3- For every three nonzero rational numbers x, y and z, if x + y is not equal to z, z is greater than both x and y, and x, y, and z are not the lengths of the sides of a right triangle, then there is a nonzero irrational number n such that x^n + y^n = z^n.
If 1-, 2- and 3- are true, then the set of irrational numbers is countable.
jahdallah 3 years ago
I discovered the following:
1- If n is a nonzero irrational number, then the equation x^n + y^n = z^n has solutions in nonzero rational numbers x, y and z.
2- If a number n is different from 0, 1,-1, 2, and -2 , then if (x1, y1, z1) and (x2, y2, z2) are any two solutions of the equation x^n + y^n = z^n such that x1, y1, z1, x2, y2 and z2 are nonzero numbers, then x1/y1 = x2/y2, x1/z1 = x2/z2 and y1/z1 = y2/z2.
jahdallah 3 years ago
Perdon, fallo mio, el documental se llam "El margen mas famoso de la historia"
gregory7885 3 years ago
CUAL ES EL NOMBRE DEL VIDEO COMPLETO?
caleman79 3 years ago
Se llama como el titulo fermat-universo matematico.
Saludos.
gregory7885 3 years ago
¡Me has dejado a medias!
Picateclas 3 years ago
Es que este video esta extraido del documental y solo es una parte que necesitaba para una presentacion en una de las asignaturas de la carrera. Pero en youtube tienes el video completo.
gregory7885 3 years ago
y como se llama el documental?
1950slollipop 3 years ago