During our study of the Beal Conjecture with my friend and fellow mathematics graduate Jonathan Beal, we looked at the equation
A^x + B^y = C^z
where A, B, C, x, y, and z are integers. As a result A^x, B^y, and C^z are integers.
Let A^x be even (where A is a multiple of 2). Let B = p*m where p is a prime number. Then B^y = p^y * m^y.
The only even prime is 2. All other prime numbers (3, 5, 7, etc. ) are odd.
So if A^x is even and
p = 2 and m is even: p^y is even, m^y is even, B^y is even, and C^z is even.
p = 2 and m is odd: p^y is even, m^y is odd, B^y is even, and C^z is even.
p ≠ 2 and m is even: p^y is odd, m^y is even, B^y is even, and C^z is even.
p ≠ 2 and m is odd: p^y is odd, m^y is odd, B^y is odd, and C^z is odd
Assuming A^x is odd and
p = 2 and m is even: p^y is even, m^y is even, B^y is even, and C^z is odd.
p = 2 and m is odd: p^y is even, m^y is odd, B^y is even, and C^z is odd.
p ≠ 2 and m is even: p^y is odd, m^y is even, B^y is even, and C^z is odd.
p ≠ 2 and m is odd: p^y is odd, m^y is odd, B^y is odd, and C^z is even.
Eddie
This blog is property of Edward Shore. 2013
A blog is that is all about mathematics and calculators, two of my passions in life.
Wednesday, September 4, 2013
Properties of A^x + B^y = C^z with Jonathan Neal
Subscribe to:
Post Comments (Atom)
HP Prime and Casio fxCG50: Trapezoid Midsegment, Height, Area
HP Prime and Casio fxCG50: Trapezoid Midsegment, Height, Area The program TRAPEZ calculates the following: Midsegment leng...

TI36X Pro Review This is a review of the TI36X Pro Calculator by Texas Instruments. History Originally, this was the TI30X Pro that w...

Casio fx991EX Classwiz Review Casio FX991EX The next incarnation of the fx991 line of Casio calculators is the fx991 EX. ...

One of the missing features of the TI82/83/84 family is the ability to convert between bases. Here are two programs in TIBasic to help...
Thank you for your post. This is excellent information. It is amazing and wonderful to visit your site. It really gives me an insight on this topic. You can find more information about residential properties here.
ReplyDelete