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Number Theory
Units digit of powers
Find the last digit of a^n using its cycle.
Practise →Modular exponentiation
Compute a^n mod m without a calculator.
Practise →Power towers (iterated Euler)
Find a^(b^c) mod m by reducing the exponent mod φ(m).
Practise →Counting divisors
How many divisors does a number have?
Practise →GCD & LCM
Least common multiples from prime structure.
Practise →Chinese Remainder
Smallest number with given remainders.
Practise →Trailing zeros of n!
Count zeros at the end of a factorial.
Practise →Perfect-square divisors
Count the divisors that are perfect squares.
Practise →Quadratic congruences
Count n in a range with m | n² + c.
Practise →Coprime factorisations
Count ways to write N = a×b with gcd(a,b)=1.
Practise →Multiplicative order
The smallest k with aᵏ ≡ 1 (mod n) — it divides φ(n).
Practise →Prime power in a binomial (Kummer)
The power of p dividing C(m, r), counted by carries in base p.
Practise →