what exactly is number theory i have heard of it but i don't know what it is
It is the study of numbers mainly (even only) about integers.
what it studyed about them and why only even numbers?
Not even numbers, just whole numbers. Jamil meant "mainly, or only, about integers", using "even" in the other sense.
ok but what about numbers dose number theory study.
Prime numbers, density of integer sequences, divisibility relations between numbers, sumsets, code design, compression, and many other things.
The properties of the natural numbers =]
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