From d2c4d7479c782fe3206f08883939ba56526dec9f Mon Sep 17 00:00:00 2001 From: Ridge Kimani Date: Sat, 30 Aug 2025 18:27:35 +0300 Subject: [PATCH 1/3] feat: fermat's last theorem test --- Maths/FermatsLastTheoremTest.js | 79 +++ Maths/test/FermatsLastTheoremTest.test.js | 29 + package-lock.json | 617 +++++++++++++--------- 3 files changed, 476 insertions(+), 249 deletions(-) create mode 100644 Maths/FermatsLastTheoremTest.js create mode 100644 Maths/test/FermatsLastTheoremTest.test.js diff --git a/Maths/FermatsLastTheoremTest.js b/Maths/FermatsLastTheoremTest.js new file mode 100644 index 0000000000..d209947c9e --- /dev/null +++ b/Maths/FermatsLastTheoremTest.js @@ -0,0 +1,79 @@ +/* + * Fermat's Last Theorem states: + * + * For every integer n >= 3, the equation + * + * x^n + y^n = z^n + * + * has no nontrivial integer solutions (x, y, z > 0). + * + * In contrast, for n = 2 there are infinitely many solutions (the famous + * Pythagorean triples like 3^2 + 4^2 = 5^2). + * + * While Andrew Wiles proved this theorem in 1994 using advanced mathematics + * (elliptic curves and modular forms), we can illustrate the theorem in JavaScript + * by brute-force checking ranges of x, y, z for small exponents n. + * + * within checked ranges, no counterexamples exist for n >= 3. + */ + +/** + * Check for counterexamples to Fermat's Last Theorem within a bounded range. + * + * This function uses BigInt arithmetic to handle large ranges safely. + * + * @param {number} maxValue - The maximum integer to check for x and y + * @param {number} exponent - The power n (>= 3) + * @returns {Array} - Array of counterexamples found (should be empty) + */ + +const checkFermatLastTheorem = (maxValue, exponent) => { + if (exponent < 3) { + throw new Error("Fermat's Last Theorem only applies for n >= 3") + } + + const counterexamples = [] + const exponentBigInt = BigInt(exponent) + + for (let baseX = 1; baseX <= maxValue; baseX++) { + const baseXPowerN = BigInt(baseX) ** exponentBigInt + + for (let baseY = baseX; baseY <= maxValue; baseY++) { + const baseYPowerN = BigInt(baseY) ** exponentBigInt + const sumOfPowers = baseXPowerN + baseYPowerN + + // compute integer nth root of sumOfPowers using binary search + let lowerBound = 1n + let upperBound = sumOfPowers + let potentialZ = 0n + + while (lowerBound <= upperBound) { + const middle = (lowerBound + upperBound) >> 1n + const middlePowerN = middle ** exponentBigInt + + if (middlePowerN === sumOfPowers) { + potentialZ = middle + break + } else if (middlePowerN < sumOfPowers) { + lowerBound = middle + 1n + } else { + upperBound = middle - 1n + } + } + + // exact check + if (potentialZ > 0n && potentialZ ** exponentBigInt === sumOfPowers) { + counterexamples.push({ + x: baseX, + y: baseY, + z: potentialZ.toString(), + n: exponent + }) + } + } + } + + return counterexamples +} + +export default checkFermatLastTheorem diff --git a/Maths/test/FermatsLastTheoremTest.test.js b/Maths/test/FermatsLastTheoremTest.test.js new file mode 100644 index 0000000000..52220df85b --- /dev/null +++ b/Maths/test/FermatsLastTheoremTest.test.js @@ -0,0 +1,29 @@ +import checkFermatLastTheorem from '../FermatsLastTheoremTest.js' +describe("Fermat's Last Theorem Checker (BigInt version)", () => { + test('throws an error if exponent is less than 3', () => { + expect(() => checkFermatLastTheorem(10, 2)).toThrow( + "Fermat's Last Theorem only applies for n >= 3" + ) + expect(() => checkFermatLastTheorem(10, 1)).toThrow() + }) + + test('small range test: returns empty array for n = 3, max 20', () => { + const results = checkFermatLastTheorem(20, 3) + expect(results).toEqual([]) + }) + + test('moderate range test: returns empty array for n = 3, max 1000', () => { + const results = checkFermatLastTheorem(1000, 3) + expect(results).toEqual([]) + }) + + test('small range test: returns empty array for n = 4, max 20', () => { + const results = checkFermatLastTheorem(20, 4) + expect(results).toEqual([]) + }) + + test('moderate range test: returns empty array for n = 4, max 500', () => { + const results = checkFermatLastTheorem(500, 4) + expect(results).toEqual([]) + }) +}) diff --git a/package-lock.json b/package-lock.json index 5c38ba06a8..648f7eccce 100644 --- a/package-lock.json +++ b/package-lock.json @@ -84,6 +84,7 @@ "ppc64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "aix" @@ -100,6 +101,7 @@ "arm" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "android" @@ -116,6 +118,7 @@ "arm64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "android" @@ -132,6 +135,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "android" @@ -148,6 +152,7 @@ "arm64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "darwin" @@ -164,6 +169,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "darwin" @@ -180,6 +186,7 @@ "arm64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "freebsd" @@ -196,6 +203,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "freebsd" @@ -212,6 +220,7 @@ "arm" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -228,6 +237,7 @@ "arm64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -244,6 +254,7 @@ "ia32" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -260,6 +271,7 @@ "loong64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -276,6 +288,7 @@ "mips64el" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -292,6 +305,7 @@ "ppc64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -308,6 +322,7 @@ "riscv64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -324,6 +339,7 @@ "s390x" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -340,6 +356,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "linux" @@ -356,6 +373,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "netbsd" @@ -372,6 +390,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "openbsd" @@ -388,6 +407,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "sunos" @@ -404,6 +424,7 @@ "arm64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "win32" @@ -420,6 +441,7 @@ "ia32" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "win32" @@ -436,6 +458,7 @@ "x64" ], "dev": true, + "license": "MIT", "optional": true, "os": [ "win32" @@ -452,6 +475,19 @@ "node": ">=8" } }, + "node_modules/@jest/schemas": { + "version": "29.6.3", + "resolved": "https://registry.npmjs.org/@jest/schemas/-/schemas-29.6.3.tgz", + "integrity": "sha512-mo5j5X+jIZmJQveBKeS/clAueipV7KgiX1vMgCxam1RNYiqE1w62n0/tJJnHtjW8ZHcQco5gY85jA3mi0L+nSA==", + "dev": true, + "license": "MIT", + "dependencies": { + "@sinclair/typebox": "^0.27.8" + }, + "engines": { + "node": "^14.15.0 || ^16.10.0 || >=18.0.0" + } + }, "node_modules/@jridgewell/gen-mapping": { "version": "0.3.3", "dev": true, @@ -528,215 +564,296 @@ } }, "node_modules/@rollup/rollup-android-arm-eabi": { - 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"nanoid": "^3.3.7", - "picocolors": "^1.1.0", + "nanoid": "^3.3.11", + "picocolors": "^1.1.1", "source-map-js": "^1.2.1" }, "engines": { @@ -1675,6 +1754,21 @@ "url": "https://github.com/prettier/prettier?sponsor=1" } }, + "node_modules/pretty-format": { + "version": "29.7.0", + "resolved": "https://registry.npmjs.org/pretty-format/-/pretty-format-29.7.0.tgz", + "integrity": "sha512-Pdlw/oPxN+aXdmM9R00JVC9WVFoCLTKJvDVLgmJ+qAffBMxsV85l/Lu7sNx4zSzPyoL2euImuEwHhOXdEgNFZQ==", + "dev": true, + "license": "MIT", + "dependencies": { + "@jest/schemas": "^29.6.3", + "ansi-styles": "^5.0.0", + "react-is": "^18.0.0" + }, + "engines": { + "node": "^14.15.0 || ^16.10.0 || >=18.0.0" + } + }, "node_modules/queue-microtask": { "version": "1.2.3", "dev": true, @@ -1695,7 +1789,9 @@ "license": "MIT" }, "node_modules/react-is": { - "version": "18.2.0", + "version": "18.3.1", + "resolved": "https://registry.npmjs.org/react-is/-/react-is-18.3.1.tgz", + "integrity": "sha512-/LLMVyas0ljjAtoYiPqYiL8VWXzUUdThrmU5+n20DZv+a+ClRoevUzw5JxU+Ieh5/c87ytoTBV9G1FiKfNJdmg==", "dev": true, "license": "MIT" }, @@ -1709,12 +1805,13 @@ } }, "node_modules/rollup": { - 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"version": "4.0.8", + "version": "4.1.0", + "resolved": "https://registry.npmjs.org/type-detect/-/type-detect-4.1.0.tgz", + "integrity": "sha512-Acylog8/luQ8L7il+geoSxhEkazvkslg7PSNKOX59mbB9cOveP5aq9h74Y7YU8yDpJwetzQQrfIwtf4Wp4LKcw==", "dev": true, "license": "MIT", "engines": { @@ -1905,13 +2014,6 @@ "dev": true, "license": "MIT" }, - "node_modules/undici-types": { - "version": "5.26.5", - "dev": true, - "license": "MIT", - "optional": true, - "peer": true - }, "node_modules/v8-to-istanbul": { "version": "9.2.0", "dev": true, @@ -1931,10 +2033,11 @@ "license": "MIT" }, "node_modules/vite": { - "version": "5.4.8", - "resolved": "https://registry.npmjs.org/vite/-/vite-5.4.8.tgz", - "integrity": "sha512-FqrItQ4DT1NC4zCUqMB4c4AZORMKIa0m8/URVCZ77OZ/QSNeJ54bU1vrFADbDsuwfIPcgknRkmqakQcgnL4GiQ==", + "version": "5.4.19", + "resolved": "https://registry.npmjs.org/vite/-/vite-5.4.19.tgz", + "integrity": "sha512-qO3aKv3HoQC8QKiNSTuUM1l9o/XX3+c+VTgLHbJWHZGeTPVAg2XwazI9UWzoxjIJCGCV2zU60uqMzjeLZuULqA==", "dev": true, + "license": "MIT", "dependencies": { "esbuild": "^0.21.3", "postcss": "^8.4.43", @@ -1990,7 +2093,9 @@ } }, "node_modules/vite-node": { - "version": "1.2.1", + "version": "1.6.1", + "resolved": "https://registry.npmjs.org/vite-node/-/vite-node-1.6.1.tgz", + "integrity": "sha512-YAXkfvGtuTzwWbDSACdJSg4A4DZiAqckWe90Zapc/sEX3XvHcw1NdurM/6od8J207tSDqNbSsgdCacBgvJKFuA==", "dev": true, "license": "MIT", "dependencies": { @@ -2011,17 +2116,18 @@ } }, "node_modules/vitest": { - "version": "1.2.1", + "version": "1.6.1", + "resolved": "https://registry.npmjs.org/vitest/-/vitest-1.6.1.tgz", + "integrity": "sha512-Ljb1cnSJSivGN0LqXd/zmDbWEM0RNNg2t1QW/XUhYl/qPqyu7CsqeWtqQXHVaJsecLPuDoak2oJcZN2QoRIOag==", "dev": true, "license": "MIT", "dependencies": { - "@vitest/expect": "1.2.1", - "@vitest/runner": "1.2.1", - "@vitest/snapshot": "1.2.1", - "@vitest/spy": "1.2.1", - "@vitest/utils": "1.2.1", + "@vitest/expect": "1.6.1", + "@vitest/runner": "1.6.1", + "@vitest/snapshot": "1.6.1", + "@vitest/spy": "1.6.1", + "@vitest/utils": "1.6.1", "acorn-walk": "^8.3.2", - "cac": "^6.7.14", "chai": "^4.3.10", "debug": "^4.3.4", "execa": "^8.0.1", @@ -2030,11 +2136,11 @@ "pathe": "^1.1.1", "picocolors": "^1.0.0", "std-env": "^3.5.0", - "strip-literal": "^1.3.0", + "strip-literal": "^2.0.0", "tinybench": "^2.5.1", - "tinypool": "^0.8.1", + "tinypool": "^0.8.3", "vite": "^5.0.0", - "vite-node": "1.2.1", + "vite-node": "1.6.1", "why-is-node-running": "^2.2.2" }, "bin": { @@ -2049,8 +2155,8 @@ "peerDependencies": { "@edge-runtime/vm": "*", "@types/node": "^18.0.0 || >=20.0.0", - "@vitest/browser": "^1.0.0", - "@vitest/ui": "^1.0.0", + "@vitest/browser": "1.6.1", + "@vitest/ui": "1.6.1", "happy-dom": "*", "jsdom": "*" }, @@ -2232,6 +2338,19 @@ "version": "1.0.2", "dev": true, "license": "ISC" + }, + "node_modules/yocto-queue": { + "version": "1.2.1", + "resolved": "https://registry.npmjs.org/yocto-queue/-/yocto-queue-1.2.1.tgz", + "integrity": "sha512-AyeEbWOu/TAXdxlV9wmGcR0+yh2j3vYPGOECcIj2S7MkrLyC7ne+oye2BKTItt0ii2PHk4cDy+95+LshzbXnGg==", + "dev": true, + "license": "MIT", + "engines": { + "node": ">=12.20" + }, + "funding": { + "url": "https://github.com/sponsors/sindresorhus" + } } } } From 9439c0a28b7cedc80bc3424ce10def236871d1be Mon Sep 17 00:00:00 2001 From: ridge-kimani Date: Sat, 30 Aug 2025 15:28:45 +0000 Subject: [PATCH 2/3] Updated Documentation in README.md --- DIRECTORY.md | 1 + 1 file changed, 1 insertion(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 5e8e1f401a..f5d53542eb 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -201,6 +201,7 @@ * [Factors](Maths/Factors.js) * [FareyApproximation](Maths/FareyApproximation.js) * [FermatPrimalityTest](Maths/FermatPrimalityTest.js) + * [FermatsLastTheoremTest](Maths/FermatsLastTheoremTest.js) * [Fibonacci](Maths/Fibonacci.js) * [FigurateNumber](Maths/FigurateNumber.js) * [FindHcf](Maths/FindHcf.js) From 598dd31cdea56dd52d6c294789551b17dd33cf89 Mon Sep 17 00:00:00 2001 From: Ridge Kimani Date: Sat, 30 Aug 2025 18:33:11 +0300 Subject: [PATCH 3/3] chore: update space --- Maths/test/FermatsLastTheoremTest.test.js | 1 + 1 file changed, 1 insertion(+) diff --git a/Maths/test/FermatsLastTheoremTest.test.js b/Maths/test/FermatsLastTheoremTest.test.js index 52220df85b..b40b713961 100644 --- a/Maths/test/FermatsLastTheoremTest.test.js +++ b/Maths/test/FermatsLastTheoremTest.test.js @@ -1,4 +1,5 @@ import checkFermatLastTheorem from '../FermatsLastTheoremTest.js' + describe("Fermat's Last Theorem Checker (BigInt version)", () => { test('throws an error if exponent is less than 3', () => { expect(() => checkFermatLastTheorem(10, 2)).toThrow(