Science Forums 2

[Don Blazys]

To: Qfwfq.

(T/T)a^x+(T/T)b^y=(T/T)c^z=a^x+b^y=c^z

is wrong because it is incomplete.

You see, the above suggests that once the greatest common factor T has been cancelled and the terms are co-prime, then it is still possible to have:
x>2, y>2 and z>2, all at the same time.

It's not!

In reality, when the terms are co-prime, we must have either:
x={1,2}, y={1,2} or z={1,2}. In other words, at least one of the three exponents must be either 1 or 2 after the greatest common factor T has been cancelled.

To put it bluntly, the above representation is lying, because it says that there is no restriction on the value of either x,y or z when in reality, there is!

It is also "lame" because it allows T=1 when in reality, 1 is not a "common factor"!

Thus, the truth comes to light only after we substitute either:

T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1)),

T(b/T)^((yln(b)/(ln(T))-1)/(ln(b)/(ln(T))-1))

or

T(c/T)^((zln(c)/(ln(T))-1)/(ln(c)/(ln(T))-1))

for one of the terms in the equation:

(T/T)a^x+(T/T)b^y=(T/T)c^z.

Note that the terms involving logarithms make a lot more sense because they actually require that the cancelled common factor T>1.

This is a very serious matter, because our present methods of representing and eliminating common factors is clearly inadequate, and should not be taught in our schools.

Don.