Number theory is the study of the set of psotive whole numbers 1,2,3,4,5,6…
Some typical number theorytic questions:
- Can the sum of two squares be a square?
- Which numbers are sums of two squares?
- Can the sum of two cubes can be a cube? Can the sum of two fourth powers be a fourth powers? $n^{th}$ power?
- A prime number is a number $p$ whose only factors are 1 and $p$.
- Number shapes, triangular numbers, square numbers …
- Twin primes.
- Primes of the form $N^2+1$.