(and thus represent independent variables, since the only common partition is then unity - a/a=1 and b/b=1
Then insert a = 1 and b = 1 into the Binomial theorem)
, but is not an integer.
This is because a and b are independent (a,b), and are therefore representable as orthogonal in two dimensions (the basis of irrational numbers being a geometric construct, mapped into the line of countable integers as an enhancement of the set of integers with a metric.... (i.e., part of the real number construct)....
For irreducible integers, a/a = b/b = 1, the relation is (1,1) for irreducible integers, providing the basis for a two dimensional vector space (and the necessity of irrational numbers not a part of the integer number line ....)
If a and b have common factors, then changing a would change b....
This is the foundation of Cartesian coordinates for real numbers (Newton proved that the Binomial Theorem holds for real numbers as well as positive integers)... Irrational numbers arise from mapping linear geometric objects (lines, areas, volumes) into the integer line; transcendental numbers (e.g. ) arise from mapping curved geometric objects (circles, ellipses, areas of... etc...) into (positive integer + irrational) line. etc., etc.....
(over, and over, and over, and over, and.....)
c cannot be an integer if a and b are positive integers in Fermat's equation for n > 2.
Fermat's equation = (?) for a,b,c,n positive integers, n > 2