The problem consists of filling in the blanks in sentences related to number theory.

1. Problem Description

The problem consists of filling in the blanks in sentences related to number theory.

2. Solution Steps

a) The numbers 1, 2, 3, 4, ... are called natural numbers or positive integers.

b) The numbers 0, 1, 2, 3, ... are called whole numbers or non-negative integers.

c) Even numbers end with the digits 0, 2, 4, 6, or

8. d) Let two consecutive odd numbers be $2n+1$ and $2n+3$ for some integer $n$. The difference between them is $(2n+3) - (2n+1) = 2$.

e) The sum of any odd number and 1 is always an even number. An odd number can be written as $2n+1$ for some integer $n$. Then $(2n+1) + 1 = 2n+2 = 2(n+1)$, which is even.

f) The three odd numbers just before 10003 are 9997, 9999, and

1

0

0

0

1. g) The four even numbers just after 8996 are 8998, 9000, 9002, and

9

0

0

4.

3. Final Answer

a) The numbers 1; 2; 3; 4; ----- are called natural numbers.

b) The numbers 0;1;2;3; ----- are called whole numbers.

c) Even numbers end with the digits 0, 2, 4, 6 or

8. d) The difference between any 2 consecutive odd numbers is

2. e) The sum of any odd number and 1 is always an even number.

f) The three odd numbers just before 10003 are 9997, 9999,

1

0

0

0

1. g) The four even numbers just after 8996 are 8998, 9000, 9002, 9004.