David M. Burton, Elementary Number Theory (7th Edition).

• Comprehensive introduction to number theory, including divisibility and digital roots.

Paul Zeitz, The Art and Craft of Problem Solving.

• Problem-solving strategies and number theory puzzles, including digit-based tricks.

Wikipedia: Divisibility rule
https://en.wikipedia.org/wiki/Divisibility_rule

• Theory and examples of divisibility tests.

Wikipedia: Digital root
https://en.wikipedia.org/wiki/Digital_root

• Explanation and properties of digital roots.

NPTEL: Introduction to Number Theory
https://nptel.ac.in/courses/111/106/111106139/

• Video lectures and notes on number theory topics.