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देवनागरीइ ब्वनेत: ल्याः सिद्धान्त तियादिसँ

थ्व पौ देवनागरीं बोट छ्यला थःमंतुं नेपाललिपिइ हिलातःगु ख। थ्व पौयात च्वसु पतिइ यंकेन्ह्यः छकः ब्वनाः पाय्छि जू/मजूगू स्वयादिसँ। 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟 (𑐀𑐒𑑂𑐐𑑂𑐬𑐾𑐖𑐷: Number Theory) 𑐮𑑂𑐫𑐵𑑅 𑐖𑑂𑐫𑐵𑐫𑐵 𑐕𑐐𑐹 𑐎𑐔𑐵 𑐏𑑅 𑐐𑐸𑐎𑐶𑐮𑐶 𑐰𑐶𑐱𑐾𑐲 𑐫𑐵𑐣𑐵𑑅 𑐥𑐹𑐬𑑂𑐞 𑐮𑑂𑐫𑐵𑑅 (Integers) 𑐰 𑐄𑐩𑐶𑐐𑐸 𑐐𑐸𑐞𑐟𑐫𑑂𑐐𑐸 𑐀𑐢𑑂𑐫𑐫𑐣 𑐖𑐸𑐂। 𑐠𑐸𑐎𑐶𑐫𑐵𑐟 "𑐐𑐞𑐶𑐟𑐫𑐵 𑐮𑐵𑐣𑐷" (Queen of Mathematics) 𑐢𑐎𑐵𑑅 𑐣𑑄 𑐩𑑂𑐴𑐳𑐷𑐎𑐶, 𑐐𑐸𑐐𑐸 𑐏𑑃 𑐣𑐵𑑄𑐖𑐵𑑅𑐩𑑂𑐴 𑐐𑐞𑐶𑐟𑐖𑑂𑐘 𑐎𑐵𑐬𑑂𑐮 𑐦𑑂𑐬𑐾𑐜𑐬𑐶𑐎 𑐐𑐵𑐄𑐳 (Carl Friedrich Gauss) 𑐣𑑄 𑐢𑐫𑐵𑐡𑐷𑐐𑐸 𑐏𑑅।^[१]

𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵 𑐩𑐹 𑐖𑑂𑐫𑐵 𑐢𑐫𑐵𑐐𑐸 "𑐮𑑂𑐫𑐵𑑅" (Numbers) 𑐟𑐫𑑂𑐐𑐸 𑐥𑑂𑐬𑐎𑐺𑐟𑐶, 𑐰𑐶𑐱𑐾𑐲 𑐫𑐵𑐣𑐵𑑅 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅 (Prime Numbers) 𑐫𑐵𑐐𑐸 𑐰𑐶𑐟𑐬𑐞 𑐰 𑐳𑐩𑐷𑐎𑐬𑐞𑐟𑐫𑑂𑐐𑐸 (Equations) 𑐴𑐮 𑐩𑐵𑐮𑐾𑐐𑐸 𑐏𑑅। 𑐣𑑂𑐴𑐵𑐥𑐵 𑐠𑑂𑐰 𑐰𑐶𑐲𑐫𑐫𑐵𑐟 "𑐀𑑄𑐎𑐐𑐞𑐶𑐟" (Arithmetic) 𑐖𑐎 𑐢𑐵𑐂𑐐𑐸 𑐏𑑅, 𑐟𑐬 𑑑𑑙𑐐𑐸 𑐱𑐟𑐵𑐧𑑂𑐡𑐷 𑐮𑐶𑐥𑐵 𑐠𑐸𑐎𑐶𑐫𑐵𑐟 "𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟" 𑐢𑐎𑐵𑑅 𑐢𑐵𑐫𑐾𑐐𑐸 𑐫𑐵𑐟।

𑐂𑐟𑐶𑐴𑐵𑐳

𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵 𑐂𑐟𑐶𑐴𑐵𑐳 𑐩𑐵𑐣𑐰 𑐳𑐨𑑂𑐫𑐟𑐵𑐫𑐵 𑐐𑐞𑐶𑐟𑐷𑐫 𑐰𑐶𑐎𑐵𑐳 𑐣𑐵𑐥 𑐳𑑂𑐰𑐵𑐣𑐵𑐔𑑂𑐰𑑄𑐐𑐸 𑐡𑐸।

𑐥𑑂𑐬𑐵𑐔𑐷𑐣 𑐎𑐵𑐮

𑐡𑐎𑐮𑐫𑑂 𑐣𑑂𑐴𑐵𑐥𑐵𑑄 𑐧𑐾𑐧𑐶𑐮𑑀𑐣 𑐰 𑐂𑐖𑐶𑐥𑑂𑐚𑐫𑐵 𑐩𑐣𑐹𑐟𑐫𑑂𑐳𑑄 𑐮𑑂𑐫𑐵𑑅𑐟𑐫𑑂𑐐𑐸 𑐐𑐸𑐞 𑐧𑐵𑐬𑐾 𑐳𑐷𑐎𑐾𑐐𑐸 𑐎𑐸𑐟𑑅 𑐫𑐵𑑅𑐐𑐸 𑐏𑐣𑐾𑐡𑐸। 𑐧𑐾𑐧𑐶𑐮𑑀𑐣𑐫𑐵 "𑐥𑑂𑐮𑐶𑐩𑑂𑐥𑐚𑐣 𑑓𑑒𑑒" (Plimpton 322) 𑐣𑐵𑑄𑐫𑐵𑐐𑐸 𑐔𑐵𑐥𑑁 (Tablet) 𑐡𑐸𑐣𑐾 "𑐥𑐵𑐂𑐠𑐵𑐐𑑀𑐬𑐶𑐫𑐣 𑐚𑑂𑐬𑐶𑐥𑐮" (Pythagorean triples) 𑐫𑐵𑐐𑐸 𑐢𑐮𑑅 𑐡𑐸, 𑐐𑐸𑐎𑐶𑑄 𑐎𑑂𑐫𑐣𑐷 𑐎𑐶 𑐂𑐩𑐶𑐐𑐸 𑐥𑐵𑐮𑐫𑑂 𑐴𑐾 $a^{2}+b^{2}=c^{2}$ 𑐫𑐵𑐐𑐸 𑐖𑑂𑐘𑐵𑐣 𑐡𑐸𑐐𑐸 𑐏𑑅।

𑐥𑑂𑐬𑐵𑐔𑐷𑐣 𑐐𑑂𑐬𑐷𑐳𑐫𑑂, 𑐫𑐸𑐎𑑂𑐮𑐶𑐜 (Euclid) 𑐣𑑄 𑐃.𑐥𑐹. 𑑓𑑐𑑐 𑐥𑐵𑐏𑐾 𑐠𑑅𑐐𑐸 𑐳𑐦𑐹 "𑐊𑐮𑐶𑐩𑐾𑐣𑑂𑐚𑑂𑐳" (Elements) 𑐫𑑂 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅𑐟 𑐀𑐮𑑂𑐫𑐵𑐏 𑐡𑐸 (Infinitude of primes) 𑐢𑐎𑐵𑑅 𑐥𑑂𑐬𑐩𑐵𑐞𑐶𑐟 𑐫𑐵𑐣𑐵𑐡𑐶𑐮। 𑐀𑐠𑐾 𑐴𑐾, "𑐫𑐸𑐎𑑂𑐮𑐶𑐜𑐫𑐵𑐐𑐸 𑐀𑐮𑑂𑐐𑑀𑐬𑐶𑐡𑐩" (Euclidean algorithm) 𑐁𑑅 𑐣𑑄 𑐣𑐶𑐐𑐸 𑐮𑑂𑐫𑐵𑑅𑐫𑐵𑐐𑐸 "𑐩𑐴𑐟𑑂𑐟𑐩 𑐳𑐩𑐵𑐥𑐰𑐬𑑂𑐟𑐎" (GCD) 𑐮𑐶𑐎𑐵𑐫𑐾𑐐𑐸 𑐡𑐎𑐮𑐫𑑂 𑐧𑐵𑑄𑐮𑐵𑑅𑐐𑐸 𑐰𑐶𑐢𑐶 𑐏𑑅।

𑐨𑐵𑐬𑐟𑐷𑐫 𑐫𑑀𑐐𑐡𑐵𑐣

𑐨𑐵𑐬𑐟𑐷𑐫 𑐐𑐞𑐶𑐟𑐖𑑂𑐘𑐟𑐫𑑂𑐳𑑄 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑑂 𑐟𑑅𑐢𑑄𑐐𑐸 𑐫𑑀𑐐𑐡𑐵𑐣 𑐧𑐶𑐫𑐵𑐟𑑅𑐐𑐸 𑐡𑐸। 𑐁𑐬𑑂𑐫𑐨𑐚 (𑑔𑑗𑑖–𑑕𑑕𑑐) 𑐰 𑐧𑑂𑐬𑐴𑑂𑐩𑐐𑐸𑐥𑑂𑐟 (𑑕𑑙𑑘–𑑖𑑖𑑘) 𑐣𑑄 "𑐜𑐵𑐫𑑀𑐦𑐾𑐣𑑂𑐚𑐵𑐂𑐣 𑐳𑐩𑐷𑐎𑐬𑐞" (Diophantine equations) 𑐴𑐮 𑐫𑐵𑐫𑐾𑐐𑐸 𑐰𑐶𑐢𑐶 𑐰𑐶𑐎𑐵𑐳 𑐫𑐵𑐟। 𑐮𑐶𑐥𑐵, 𑐨𑐵𑐳𑑂𑐎𑐬 𑐡𑑂𑐰𑐶𑐟𑐷𑐫 (𑑑𑑑𑑑𑑔–𑑑𑑑𑑘𑑕) 𑐣𑑄 "𑐥𑐾𑐮𑐫𑐵𑐐𑐸 𑐳𑐩𑐷𑐎𑐬𑐞" (Pell's equation) 𑐴𑐮 𑐫𑐵𑐫𑐾𑐐𑐸 "𑐔𑐎𑑂𑐬𑐰𑐵𑐮 𑐰𑐶𑐢𑐶" (Chakravala method) 𑐰𑐶𑐎𑐵𑐳 𑐫𑐵𑐟।

𑐁𑐢𑐸𑐣𑐶𑐎 𑐎𑐵𑐮

𑑑𑑗𑐐𑐸 𑐱𑐟𑐵𑐧𑑂𑐡𑐷𑐂 𑐦𑑂𑐬𑐵𑐣𑑂𑐳𑐾𑐮𑐷 𑐐𑐞𑐶𑐟𑐖𑑂𑐘 𑐥𑐶𑐫𑐬𑐾 𑐡 𑐦𑐬𑑂𑐩𑐵 (Pierre de Fermat) 𑐣𑑄 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵𑐟 𑐴𑐵𑐣𑑄 𑐧𑑂𑐰𑑄𑐎𑐵𑐡𑐶𑐮। 𑐰𑐫𑑂𑐎𑑅𑐫𑐵 "𑐦𑐬𑑂𑐩𑐵𑐫𑐵𑐐𑐸 𑐀𑐣𑑂𑐟𑐶𑐩 𑐳𑐵𑐢𑑂𑐫" (Fermat's Last Theorem) 𑐐𑐞𑐶𑐟𑐫𑐵 𑐡𑐎𑐮𑐫𑑂 𑐣𑐵𑑄𑐖𑐵𑑅𑐐𑐸 𑐳𑐩𑐳𑑂𑐫𑐵 𑐩𑐢𑑂𑐫𑐾 𑐕𑐐𑐹 𑐏𑑅। 𑑑𑑘𑐐𑐸 𑐱𑐟𑐵𑐧𑑂𑐡𑐷𑐂 𑐮𑐶𑐫𑑀𑐣𑐵𑐬𑑂𑐜 𑐫𑐸𑐮𑐬 (Leonhard Euler) 𑐣𑑄 "𑐰𑐶𑐱𑑂𑐮𑐾𑐲𑐞𑐵𑐟𑑂𑐩𑐎 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟" (Analytic number theory) 𑐫𑐵𑐐𑐸 𑐥𑐮𑐶𑐳𑑂𑐠𑐵 𑐫𑐵𑐣𑐵𑐡𑐶𑐮।^[२]

𑐩𑐹 𑐎𑐔𑐵𑐟

𑐁𑐢𑐸𑐣𑐶𑐎 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵𑐟 𑐠𑐷𑐠𑐷 𑐎𑐔𑐵𑐫𑑂 𑐧𑑂𑐰𑐠𑐮𑐾 𑐕𑐶𑑄:

𑑑. 𑐥𑑂𑐬𑐵𑐬𑐩𑑂𑐨𑐶𑐎 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟 (Elementary Number Theory)

𑐠𑑂𑐰 𑐎𑐔𑐵𑐫𑑂 𑐩𑐾𑐩𑐾𑐐𑐸 𑐖𑐚𑐶𑐮 𑐐𑐞𑐶𑐟𑐷𑐫 𑐰𑐶𑐢𑐶 (𑐐𑐠𑐾𑐎𑐶 𑐎𑑂𑐫𑐵𑐮𑐎𑐸𑐮𑐳) 𑐩𑐕𑑂𑐫𑐳𑐾𑑄, 𑐎𑐾𑐰𑐮 𑐀𑐒𑑂𑐎𑐐𑐞𑐶𑐟𑐫𑐵 𑐁𑐢𑐵𑐬𑐫𑑂 𑐮𑑂𑐫𑐵𑑅𑐟𑐫𑑂𑐐𑐸 𑐀𑐢𑑂𑐫𑐫𑐣 𑐖𑐸𑐂। 𑐠𑐸𑐎𑐶𑐮𑐶 𑐰𑐶𑐨𑐵𑐖𑑂𑐫𑐟𑐵 (Divisibility), 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅, 𑐰 𑐩𑑀𑐜𑐸𑐮𑐬 𑐀𑐒𑑂𑐎𑐐𑐞𑐶𑐟 (Modular arithmetic) 𑐮𑐵। 𑐫𑐸𑐮𑐬𑐫𑐵𑐐𑐸 𑐳𑐵𑐢𑑂𑐫 (Euler's theorem) 𑐰 "𑐦𑐬𑑂𑐩𑐵𑐫𑐵𑐐𑐸 𑐔𑐶𑐢𑑄𑐐𑐸 𑐳𑐵𑐢𑑂𑐫" (Fermat's Little Theorem) 𑐠𑐸𑐎𑐶𑐫𑐵 𑐡𑐳𑐸 𑐏𑑅।

𑑒. 𑐰𑐶𑐱𑑂𑐮𑐾𑐲𑐞𑐵𑐟𑑂𑐩𑐎 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟 (Analytic Number Theory)

𑐠𑑂𑐰 𑐎𑐔𑐵𑐫𑑂 𑐎𑑂𑐫𑐵𑐮𑐎𑐸𑐮𑐳 (Calculus) 𑐰 𑐎𑐩𑑂𑐥𑑂𑐮𑐾𑐎𑑂𑐳 𑐊𑐣𑐵𑐮𑐶𑐳𑐶𑐳 (Complex analysis) 𑐕𑑂𑐫𑐮𑐵𑑅 𑐥𑐹𑐬𑑂𑐞 𑐮𑑂𑐫𑐵𑑅𑐟𑐫𑑂𑐐𑐸 𑐳𑐩𑐳𑑂𑐫𑐵 𑐴𑐮 𑐫𑐵𑐂। "𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅 𑐳𑐵𑐢𑑂𑐫" (Prime Number Theorem), 𑐐𑐸𑐎𑐶𑑄 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅𑐟 𑐐𑐠𑐾 𑐰𑐶𑐟𑐬𑐞 𑐖𑐸𑐫𑐵𑐔𑑂𑐰𑑄𑐐𑐸 𑐡𑐸 𑐢𑐫𑐵𑐐𑐸 𑐏𑑃 𑐳𑐷𑐎𑐾𑐟 𑐐𑑂𑐰𑐵𑐴𑐵𑐮𑐶 𑐫𑐵𑐂, 𑐠𑑂𑐰 𑐎𑐔𑐵𑐫𑐵𑐐𑐸 𑐩𑐹 𑐄𑐥𑐮𑐧𑑂𑐢𑐷 𑐏𑑅। 𑐬𑐶𑐩𑑂𑐫𑐵𑐣 𑐥𑐬𑐶𑐎𑐮𑑂𑐥𑐣𑐵 (Riemann Hypothesis) 𑐠𑑂𑐰 𑐎𑐔𑐵𑐫𑐵 𑐡𑐎𑐮𑐫𑑂 𑐟𑑅𑐢𑑄𑐐𑐸 𑐰 𑐁𑑅𑐟𑐎𑑄 𑐴𑐮 𑐩𑐖𑐹𑐐𑐸 𑐳𑐩𑐳𑑂𑐫𑐵 𑐏𑑅।^[३]

𑑓. 𑐧𑐷𑐖𑐐𑐞𑐶𑐟𑐷𑐫 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟 (Algebraic Number Theory)

𑐠𑑂𑐰 𑐎𑐔𑐵𑐫𑑂 𑐧𑐷𑐖𑐐𑐞𑐶𑐟𑐷𑐫 𑐳𑑄𑐬𑐔𑐣𑐵𑐟 (𑐐𑐠𑐾𑐎𑐶 Rings, Fields) 𑐕𑑂𑐫𑐮𑐵𑑅 𑐮𑑂𑐫𑐵𑑅𑐟𑐫𑑂𑐐𑐸 𑐀𑐢𑑂𑐫𑐫𑐣 𑐖𑐸𑐂।

𑐩𑐹 𑐀𑐰𑐢𑐵𑐬𑐞𑐵𑐟

𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅 (Prime Numbers): 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵 𑐖𑐐 𑐢𑐫𑐵𑐐𑐸 𑐴𑐾 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅 𑐏𑑅। 𑑑 𑐳𑑂𑐰𑐫𑐵 𑐟𑑅𑐢𑑄𑐐𑐸 𑐀𑐖𑑂𑐫𑐵𑑅𑐐𑐸 𑐥𑐹𑐬𑑂𑐞 𑐮𑑂𑐫𑐵𑑅, 𑐐𑐸𑐎𑐶𑐫𑐵𑐟 𑑑 𑐰 𑐠𑑅 (Self) 𑐟𑑂𑐰𑐟𑐵𑑅 𑐩𑐾𑐐𑐸 𑐮𑑂𑐫𑐵𑐏𑑄 𑐧𑑂𑐰𑐠𑐮𑐾 𑐦𑐿𑐩𑐏𑐸, 𑐄𑐎𑐶𑐫𑐵𑐟 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅 𑐢𑐵𑐂 (𑐡𑐳𑐸: 𑑒, 𑑓, 𑑕, 𑑗, 𑑑𑑑...)। "𑐀𑐒𑑂𑐎𑐐𑐞𑐶𑐟𑐫𑐵𑐐𑐸 𑐁𑐢𑐵𑐬𑐨𑐹𑐟 𑐳𑐵𑐢𑑂𑐫" (Fundamental Theorem of Arithmetic) 𑐎𑐠𑑄, 𑐴𑐬𑐾𑐎 𑑑 𑐳𑑂𑐰𑐫𑐵 𑐟𑑅𑐢𑑄𑐐𑐸 𑐥𑐹𑐬𑑂𑐞 𑐮𑑂𑐫𑐵𑑅𑐫𑐵𑐟 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅𑐟𑐫𑑂𑐐𑐸 𑐐𑐸𑐞𑐣𑐦𑐮𑐫𑐵 𑐬𑐸𑐥𑐫𑑂 𑐧𑑂𑐰𑐠𑐮𑐾 𑐕𑐶𑑄 (𑐡𑐳𑐸: $12=2\times 2\times 3$ )।

𑐩𑑀𑐜𑐸𑐮𑐬 𑐀𑐒𑑂𑐎𑐐𑐞𑐶𑐟 (Modular Arithmetic): 𑐠𑐸𑐎𑐶𑐫𑐵𑐟 "𑐑𑐜𑐷 𑐐𑐞𑐶𑐟" (Clock math) 𑐣𑑄 𑐢𑐵𑐂। 𑐠𑐸𑐎𑐶𑐮𑐶 𑐮𑑂𑐫𑐵𑑅𑐟 𑐕𑐐𑐹 𑐣𑐶𑐱𑑂𑐔𑐶𑐟 𑐩𑐵𑐣 (Modulus) 𑐠𑑂𑐫𑐣𑐾𑐰𑑄 𑐴𑐵𑐣𑑄 "𑐱𑐹𑐣𑑂𑐫" (𑑐) 𑐫𑑂 𑐮𑐶𑐴𑐵𑑃 𑐰𑐂। 𑐡𑐳𑐸: 𑑑𑑒 𑐑𑐜𑐷𑐂, 𑑑𑑓 𑐟𑐵 𑐃 𑐖𑐸𑐂𑐐𑐸 𑐢𑐫𑐵𑐐𑐸 𑑑 𑐟𑐵 𑐃 𑐖𑐸𑐂𑐐𑐸 𑐏𑑅। 𑐠𑐸𑐎𑐶𑐫𑐵𑐟 𑐐𑐞𑐶𑐟𑐫𑑂 $13\equiv 1{\pmod {12}}$ 𑐢𑐎𑐵𑑅 𑐔𑑂𑐰𑐂।

𑐕𑑂𑐫𑐾𑐮𑐾𑐖𑑂𑐫𑐵

𑐣𑑂𑐴𑐵𑐥𑐵 𑐣𑑂𑐴𑐵𑐥𑐵 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵𑐟 "𑐱𑐸𑐡𑑂𑐢 𑐐𑐞𑐶𑐟" (Pure Math) 𑐢𑐵𑐂𑐐𑐸 𑐏𑑅 𑐰 𑐠𑐸𑐎𑐶𑐫𑐵 𑐰𑑂𑐫𑐵𑐰𑐴𑐵𑐬𑐶𑐎 𑐕𑑂𑐫𑐾𑐮𑐾𑐖𑑂𑐫𑐵 𑐩𑐡𑐸 𑐢𑐎𑐵𑑅 𑐟𑐵𑐫𑐾𑐎𑐷𑐐𑐸 𑐏𑑅। 𑐟𑐬, 𑐎𑐩𑑂𑐥𑑂𑐫𑐸𑐚𑐬 𑐫𑐸𑐐𑐫𑑂 𑐠𑐸𑐎𑐶𑐫𑐵 𑐩𑐴𑐟𑑂𑐟𑑂𑐰 𑐟𑐳𑐎𑑄 𑐀𑐥𑑂𑐰𑐫𑐵 𑐰𑑅𑐐𑐸 𑐡𑐸।

𑐎𑐹𑐚𑐮𑐾𑐏𑐣 (Cryptography): 𑐂𑐣𑑂𑐚𑐬𑐣𑐾𑐚𑐫𑑂 𑐳𑐸𑐬𑐎𑑂𑐲𑐶𑐟 𑐳𑐘𑑂𑐔𑐵𑐬 (Secure Communication) 𑐫𑐵𑐫𑐾𑐟 𑐮𑑂𑐫𑐵𑑅 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵 𑐥𑑂𑐬𑐫𑑀𑐐 𑐖𑐸𑐂। 𑐡𑐳𑐸: "RSA 𑐂𑐣𑑂𑐎𑑂𑐬𑐶𑐥𑑂𑐳𑐣" (RSA Encryption) 𑐫𑑂 𑐟-𑐟𑑅𑐢𑑄𑐐𑐸 𑐀𑐨𑐵𑐖𑑂𑐫 𑐮𑑂𑐫𑐵𑑅𑐟𑐫𑑂𑐐𑐸 𑐐𑐸𑐞𑐣𑐦𑐮 𑐮𑐶𑐎𑐵𑐫𑐾𑐐𑐸 (Factorization) 𑐠𑐵𑐎𑐸𑐂𑐐𑐸 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟𑐫𑐵𑐟 𑐕𑑂𑐫𑐮𑐷।^[४]
𑐎𑑀𑐜𑐶𑐒 𑐳𑐶𑐡𑑂𑐢𑐵𑐣𑑂𑐟 (Coding Theory): 𑐜𑐵𑐚𑐵 (Data) 𑐳𑐘𑑂𑐔𑐵𑐬 𑐫𑐵𑐫𑐾𑐐𑐸 𑐂𑐮𑐫𑑂 𑐖𑐸𑐂𑐐𑐸 𑐐𑐮𑑂𑐟𑐷 (Errors) 𑐳𑐸𑐢𑐵𑐬 𑐫𑐵𑐫𑐾𑐟 𑐠𑐸𑐎𑐶𑐫𑐵 𑐥𑑂𑐬𑐫𑑀𑐐 𑐖𑐸𑐂।

𑐮𑐶𑐢𑑄𑐳𑐵

↑ Gauss, C. F. (1801). Disquisitiones Arithmeticae.
↑ Burton, David M. (2010). Elementary Number Theory. McGraw-Hill.
↑ Apostol, Tom M. (1976). Introduction to Analytic Number Theory. Springer.
↑ Koblitz, Neal (1994). A Course in Number Theory and Cryptography. Springer.

𑐥𑐸𑐔𑑅:𑐮𑑂𑐫𑐵𑑅 𑐖𑑂𑐫𑐵 𑐥𑐸𑐔𑑅:𑐐𑐞𑐶𑐟

[Gauss-1] Gauss, C. F. (1801). Disquisitiones Arithmeticae.

[Burton-2] Burton, David M. (2010). Elementary Number Theory. McGraw-Hill.

[3] Apostol, Tom M. (1976). Introduction to Analytic Number Theory. Springer.

[4] Koblitz, Neal (1994). A Course in Number Theory and Cryptography. Springer.

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