Pythagoreom Triplets and Fermats last Theormem???

Question

Okay, for homework I have to say if each one of these is true or false.

x^3+y^3=z^3...True or False and give an example if its true.

x^4+y^4=z^4..." "

My teacher said that I could look on the internet or guess and test on my own. I've tried both but I can't find anything. Anyone know if either one of these is true, and if so what's an example of it.

Answer 1

First let us take Fermat Theorem: Theorem # 4: x^4 + y^4 = z^4 has no solution in NATURAL NUMBERS.

So x ^ 4 + y^4 = z^4 is FALSE for any x, y, z being natural numbers.

So, no example can be given to prove this equation.

For The Proof of the theorem. refer to the following site:



Recently, I saw a research work DISPROVING FERMAT'S Last Theorem by one by I. Savant of Marietta, Georgia..

The THEOREM: "When n> (is greater than) 2, there exists no solution for the EQUATION:

A^ n + B ^ n = C ^ n."

For x^3 + y ^3 = z ^ 3, there are some very near solutions given:

1.
64 ^3 + 94 ^ 3 = 103 ^ 3. (with very negligible variance of (0.0000915 %). There are other examples given in the site below.

Please check how far they are NEAR TRUE (according to IDIOTHEOREM)

Source:

http://72.14.253.104/search?q=cache:UbMYPpP5hlwJ:home.mindspring.com/~jbshand/ferm.html+Fermat+Theorem&hl=en&gl=us&ct=clnk&cd=5


Hope this helps you.

Gimme my TENNER if this answer is helpful.

Answer 2

You have a cruel teacher. Fermat proved the second one. The other one was proven recently. Wikipedia has an article on Fermat's Last Theorem that talks about that, but I don't think it gives examples.

Answer 3

I'd imagine it's true, unless x, y, and z are static (non-changing) variables. The basic principle is that one of the values (we'll use z) will change every time you increase the degree of the equation. For example, let's say that x=2 and y=3.
2^3 + 3^3 = z^3
8 + 27 = z^3
35 = z^3
z equals the cube root of 35.

You could concievably do the same process for the fourth power, etc.

Answer 4

If you mean: Do either of these equations
have a solution in INTEGERS, both only do
when one of the variables is 0.
Fermat verified the second by using the method
of infinite descent(which you might want to look up).