A beginning tudent in number theory could start with mathematical induction because it is essentially the definition of the natural numbers but for some reason it is considered difficult. With that the fundamental theorem can be proved and we can start number theory. Alternatively a more concrete approach is to start with numbers dividing each other and those with remainders, which leads to the notion of greatest common divisor and Bezout's Lemma, this can also lead to a proof of the fundamental theorem. The arithmetic with remainders is an interesting gem discovered along the way and can be considered central to number theory as well. This is modular arithmetic and we learn how to deal with calculations there using Euler's theorem.