https://h30306.github.io/blog/tags/number-theory/Recent content in Number-Theory onHugo -- gohugo.ioenhwork0511@gmail.com (Wei Yi Chung)hwork0511@gmail.com (Wei Yi Chung)© 2026 Wei Yi ChungMon, 02 Nov 2026 00:00:00 +0000https://h30306.github.io/blog/leetcode/leetcode-4098/Mon, 02 Nov 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-4098/LeetCode 4098 note: value’s smallest prime factor p decides everything: the next element is at least value + p, then even numbers step by 2; the left side is feasible iff value - p >= 2 * indexhttps://h30306.github.io/blog/algorithm/number-theory/Tue, 20 Oct 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/algorithm/number-theory/GCD, primality tests, the sieve of Eratosthenes / linear sieve / smallest prime factor (SPF), connecting numbers by prime factors with Union-Find, and splitting an array by the last occurrence of prime factorshttps://h30306.github.io/blog/leetcode/leetcode-2584/Tue, 13 Oct 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-2584/LeetCode 2584 note: coprime products ⇔ no prime factor in both parts; record each prime’s last index, extend reach left to right, and split after i when reach == ihttps://h30306.github.io/blog/leetcode/leetcode-4081/Tue, 13 Oct 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-4081/LeetCode 4081 note: sieve the primes, then 0/1 knapsack with dp[j] the fewest primes summing to j; adding primes from large to small, a tie gives a smaller first element, so updating on <= yields the lexicographically smallesthttps://h30306.github.io/blog/leetcode/leetcode-1998/Mon, 12 Oct 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-1998/LeetCode 1998 note: numbers in one component can be permuted freely; union each number with its prime factors via SPF, and the array sorts iff each position’s old and new values share a grouphttps://h30306.github.io/blog/leetcode/leetcode-2523/Mon, 12 Oct 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-2523/LeetCode 2523 note: sieve the primes in range, since only adjacent primes can be closest; or trial-divide rightward from left and stop at the first twin primes with gap 2https://h30306.github.io/blog/leetcode/leetcode-2761/Mon, 12 Oct 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-2761/LeetCode 2761 note: sieve primes below n, then try x up to n / 2; when x and n - x are both prime, they form a pairhttps://h30306.github.io/blog/leetcode/leetcode-1627/Sat, 05 Sep 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-1627/LeetCode 1627 note: no pairwise GCDs; for each z > threshold, connect all multiples of z, O(n log n) unions in totalhttps://h30306.github.io/blog/leetcode/leetcode-3984/Mon, 06 Jul 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-3984/LeetCode 3984 note: replacing a composite k by one of its prime factors only helps (more values divisible, smaller k), so try every prime factor of the numbers plus 2, running Kadane once per candidatehttps://h30306.github.io/blog/leetcode/leetcode-3918/Sun, 03 May 2026 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-3918/LeetCode 3918 note: reverse n, take the range [min, max], and sum primes by trial division; test divisibility with %, never by comparing // with /https://h30306.github.io/blog/leetcode/leetcode-2413/Wed, 17 Dec 2025 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-2413/LeetCode 2413 note: lcm(2, n), which is n when n is even and 2n when oddhttps://h30306.github.io/blog/leetcode/leetcode-2709/Thu, 07 Aug 2025 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-2709/LeetCode 2709 note: every pair of indices connects ⇔ one component; factor with SPF and union each number with its prime factors in Union-Find, treating 1 speciallyhttps://h30306.github.io/blog/leetcode/leetcode-3618/Sat, 19 Jul 2025 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-3618/LeetCode 3618 note: primality is about the index; a sieve of Eratosthenes marks all of 0..n-1 at once, faster than trial division per indexhttps://h30306.github.io/blog/leetcode/leetcode-1979/Sat, 17 May 2025 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-1979/LeetCode 1979 note: find the minimum and maximum, then take their GCD with Euclid’s algorithmhttps://h30306.github.io/blog/leetcode/leetcode-952/Sat, 10 May 2025 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-952/LeetCode 952 note: sharing a factor ⇔ sharing a prime factor; factor each number and union indices with the same prime factor using Union-Find, with no pairwise GCDshttps://h30306.github.io/blog/leetcode/leetcode-204/Fri, 11 Nov 2022 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-204/LeetCode 204 note: the sieve of Eratosthenes, crossing out multiples of each prime p starting at p², with the outer loop only up to √nhttps://h30306.github.io/blog/leetcode/leetcode-258/Mon, 22 Aug 2022 00:00:00 +0000hwork0511@gmail.com (Wei Yi Chung)https://h30306.github.io/blog/leetcode/leetcode-258/LeetCode 258 note: sum the digits repeatedly until one remains; the O(1) answer is the digital root 1 + (n - 1) % 9