➗ Math

One-line summary: Number theory, combinatorics, and arithmetic tricks — the foundation of competitive programming warm-ups.

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Key Topics

Topic	Key Insight
GCD / LCM	Euclidean: gcd(a,b) = gcd(b, a%b)
Sieve of Eratosthenes	Find all primes ≤ n in O(n log log n)
Modular Arithmetic	(a+b)%m = ((a%m)+(b%m))%m
Combinatorics	nCr = n! / (r! * (n-r)!)
Trailing zeros in n!	Count factor-5s: ⌊n/5⌋ + ⌊n/25⌋ + ...
Perfect square	Math.sqrt(n) % 1 === 0
Fibonacci

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Common Patterns

GCD / LCM

function gcd(a, b) {
  return b === 0 ? a : gcd(b, a % b);
}
function lcm(a, b) {
  return (a / gcd(a, b)) * b;
}

Sieve of Eratosthenes

function sieve(n) {
  const p = new Array(n + 1).fill(true);
  p[0] = p[1] = false;
  for (let i = 2; i * i <= n; i++) if (p[i]) for (let j = i * i; j <= n; j += i) p[j] = false;
  return p;
}

Trailing Zeros

function trailingZeros(n) {
  let c = 0;
  while (n >= 5) {
    n = Math.floor(n / 5);
    c += n;
  }
  return c;
}

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Practice Problems

Easy Problems

Problem	Difficulty	Solution
LC 7 — Reverse Integer	Easy
LC 9 — Palindrome Number	Easy
LC 13 — Roman to Integer	Easy
LC 66 — Plus One	Easy
LC 69 — Sqrt(x)	Easy
LC 168 — Excel Sheet Column Title	Easy
LC 171 — Excel Sheet Column Number	Easy
LC 202 — Happy Number	Easy
LC 231 — Power of Two	Easy
LC 258 — Add Digits	Easy
LC 263 — Ugly Number	Easy
LC 326 — Power of Three	Easy
LC 342 — Power of Four	Easy
LC 367 — Valid Perfect Square	Easy
LC 415 — Add Strings	Easy
LC 441 — Arranging Coins	Easy
LC 507 — Perfect Number	Easy
LC 509 — Fibonacci Number	Easy	View Solution
LC 728 — Self Dividing Numbers	Easy
LC 1137 — N-th Tribonacci Number	Easy
LC 1175 — Prime Arrangements	Easy
LC 1281 — Subtract the Product and Sum of Digits	Easy
LC 1317 — Convert Integer to the Sum of Two No-Zero Integers	Easy
LC 1323 — Maximum 69 Number	Easy
LC 1360 — Number of Days Between Two Dates	Easy
CC — Add Two Numbers (FLOW001)	Easy
CC — Small Factorials (FLOW018)	Easy
CC — First and Last Digit (FLOW004)	Easy
CC — Sum of Digits (FLOW006)	Easy
CC — GCD and LCM (FLOW016)	Easy
CC — Prime Generator (PRIME1)	Easy
CC — Reverse Number (REVNUM)	Easy
LC 12 — Integer to Roman	Medium
LC 29 — Divide Two Integers	Medium
LC 43 — Multiply Strings	Medium
LC 50 — Pow(x, n)	Medium
LC 166 — Fraction to Recurring Decimal	Medium
LC 172 — Factorial Trailing Zeroes	Medium
LC 204 — Count Primes	Medium
LC 264 — Ugly Number II	Medium
LC 279 — Perfect Squares	Medium
LC 319 — Bulb Switcher	Medium
LC 365 — Water and Jug Problem	Medium
LC 372 — Super Pow	Medium
LC 396 — Rotate Function	Medium
LC 470 — Implement Rand10 Using Rand7	Medium
LC 593 — Valid Square	Medium
LC 633 — Sum of Square Numbers	Medium
LC 754 — Reach a Number	Medium
LC 780 — Reaching Points	Medium
LC 829 — Consecutive Numbers Sum	Medium
LC 858 — Mirror Reflection	Medium
LC 914 — X of a Kind in a Deck of Cards	Medium
LC 1006 — Clumsy Factorial	Medium
LC 1217 — Minimum Cost to Move Chips to The Same Position	Medium
LC 1390 — Four Divisors	Medium
CC — Modular Exponentiation (MODEX)	Medium
CC — Catalan Numbers (CATALAN)	Medium
CC — Number Theory (NUMTHEORY)	Medium
LC 60 — Permutation Sequence	Hard
LC 149 — Max Points on a Line	Hard
LC 233 — Number of Digit One	Hard
LC 335 — Self Crossing	Hard
LC 391 — Perfect Rectangle	Hard
LC 458 — Poor Pigs	Hard
LC 564 — Find the Closest Palindrome	Hard
LC 587 — Erect the Fence	Hard
LC 679 — 24 Game	Hard
LC 753 — Cracking the Safe	Hard
LC 810 — Chalkboard XOR Game	Hard
LC 887 — Super Egg Drop	Hard
LC 906 — Super Palindromes	Hard
LC 1012 — Numbers With Repeated Digits	Hard
LC 1088 — Confusing Number II	Hard
LC 1363 — Largest Multiple of Three	Hard
LC 1397 — Find All Good Strings	Hard
CC — Advanced Number Theory (ADVNUM)	Hard
CC — Chinese Remainder Theorem (CRT)	Hard
CC — Extended Euclidean (EXTEUC)	Hard

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Related Topics

• School Basics — primes, GCD, factorial
• Bit Manipulation — arithmetic bit tricks

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