Advanced High-School Mathematics

Chapter 2

Discrete Mathematics

2.1 Elementary Number Theory

While probably an oversimplication, “number theory” can be said to
be concerned with the mathematics of the ordinary whole numbers:

0 ,± 1 ,± 2 , ....

We shall, for convenience denote the set of whole numbers byZ.

Notice that the famousFermat conjecture^1 falls into this context,
as it asserts that

For any integern≥ 3 , the equation

xn+yn=zn

has no solution with x, y, z ∈ Z

withx, y, z 6 = 0.

Of course, the assertion is false withn= 1 or 2 as, for instance, 3^2 +4^2 =
52.

(^1) which was proved by Andrew Wiles in 1995
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