Number theory is the study of the set of positive whole numbers.
Let’s start with some definitions to help us gain a basic understanding of number theory:
Natural numbers are numbers used for counting:
Whole numbers include all natural numbers and 
: 
Integers include all whole numbers and their negative
counterpart: 
Exponentiation 
the k-th power of
is the repeated multiplication
of 
by 
times:
In is the
base and is the exponent. The square of is 
The cube of is 
A perfect square is an integer that is the square of another integer. A perfect cube is an integer that is the cube of another integer.
If 
and 
, 
if 
Problem 2‑1
2000 numbers 
are chosen from one of
the three values: 
If 
and 
what is the value of 
Solution:
Don’t let the long sequence of tricks you to believe
that this is a complex problem. In elementary school, we learned that multiplication
is repeated addition. Since 
can
only take three values, to solve the problem, we only need to figure out the
numbers of 
and 
in
the sequence. Let 
be the number of 
and 
be the
number of 
We don’t need to include
as 
The original problem is
converted to a two-variable linear equation problem:
Therefore,
General
Rule: Multiplication is repeated addition. 