I am writing an introduction to a first course in elementary number theory. The topics are linear Diophantine equations, modular arithmetic including FLT and Euler's Generalization, quadratic residues and Non - linear Diophantine equations.
How can I write an introduction to this showing linkage between the various topics and hook potential students to do this course? What is the motivation on covering these topics?

I am writing an introduction to a first course in elementary number theory.
The topics are linear Diophantine equations, modular arithmetic including FLT and Euler's Generalization,
quadratic residues and Non - linear Diophantine equations.
How can I write an introduction to this showing linkage between the various topics and hook potential students to do this course?
What is the motivation on covering these topics?