NUMBER THEORY

What Number Theory means on the AMC10

Number theory questions are about the structure of the integers. The most common tools:

• Divisibility and primes — divisibility tests, prime factorization
• GCD and LCM — the relationship $\gcd(a,b)\cdot\mathrm{lcm}(a,b) = a\cdot b$
• Modular arithmetic — solving "what is the remainder when..." problems quickly
• Digit problems — units digit, sum of digits, palindromes
• Number bases — converting and reasoning in non-base-10

A surprising fraction of these problems collapse to mod 9 or mod 10 tricks once you spot the pattern.