Is the multiplication of 2002 consecutive natural numbers odd or even? Is the multiplication of 2002 consecutive natural numbers odd or even? Why?

Is the multiplication of 2002 consecutive natural numbers odd or even? Is the multiplication of 2002 consecutive natural numbers odd or even? Why?

The multiplication of 2002 continuous natural numbers is even
Odd * even = even

One of the following four numbers is the product of two adjacent natural numbers. What is the number? A, 1980, B, 1995, C, 1998, D, 2003

A
44×45=1980

The product of two natural numbers a and B of Diophantine equation is smaller than the square of a number. How many groups of natural numbers satisfy this condition?
Using Diophantine equation

x(x-y)=1995
1995=5*3*7*19
x=665 y=662 x=399 y=394 x=285 y=278 x=105 y=86 x=133 y=118 x=57 y=22 x=95 y=74 x=1995 y=1