be positive real numbers . Prove that
Y by son7, Functional_equation, Tumon2001, Arabian_Math, Rg230403, amar_04, N0_NAME, bissue, XbenX, IAmTheHazard, TETris5, niyu, vsamc, MathPassionForever, anantmudgal09, MathBoy23, Spaced_Out, nikenissan, Abhaysingh2003, OlympusHero, Aryan-23, srijonrick, ETS1331, Ilove_mathematics, NumberX, Kar-98k, ayan.nmath, Kanep, Martin007B, Pluto1708, SnowPanda, anonman, myh2910, EulersTurban, Steve12345, TurtleKing123, mijail, VipMath, etvat, pog, Bassiskicking, v4913, amuthup, Jafarly8097, ilovepizza2020, NCEE, Eat314, itslumi, pad, mira74, samuel, porkemon2, Ultimate_Drinker, andyxpandy99, mathleticguyyy, matharcher, fidgetboss_4000, Jay17, rachelshi, hsiangshen, justin1228, Kagebaka, Imayormaynotknowcalculus, insertionsort, Zorger74, ghu2024, jacoporizzo, Jerry122805, Bumblebee60, MNJ2357, fukano_2, leibnitz, Ninjasolver0201, RMOAspirantFaraz, 508669, ELMOliveslong, Siddharth03, NJOY, dangerousliri, Ucchash, ApraTrip, rcorreaa, mathsworm, yayitsme, jj_ca888, Aimingformygoal, SHREYAS333, TortilloSquad, carzland, Math-wiz, Dem0nfang, 606234, mueller.25, IMOTC, lilavati_2005, mathtiger6, GeoMetrix, TheMath_boy, DAWAE, IndoMathXdZ, jelena_ivanchic, hellomath010118, A-Thought-Of-God, k12byda5h, Andrei246, BlobbytheBlob12, Aritra12, freeman66, Math00954, fjm30, Aarth, TheMathsBoy, Kimchiks926, mathsfun28, Mathphile01, InternetPerson10, RandomTraveller, Jupiter_is_BIG, hansu, Dodgers66, Keith50, p_square, geometry6, hyay, Mathlete12345654, TheDarkPrince, quirtt, Kyleray, MathX322, khina, Math_pi_thon, Bunrong123, lrjr24, Apocellipse, Aniruddha07, Delta0001, naman12, star-1ord, Mr.C, AforApple, Pigeonhole_Biswaranjan_, Wavefunction, SenorIncongito, EmilXM, Gottfried25, nikaaryu, The_Maitreyo1, RudraRockstar, gamerrk1004, Dr_Vex, CaptainLevi16, third_one_is_jerk, coolmath_2018, agile_eagle, AdithyaU89, heheXD1, Sedro, sriraamster, Supercali, biomathematics, Jan17103, Ha_ha_ha, AKS_9_54_61, Atpar, Williamgolly, MathJams, Sumedha_Maths, Pluto04, angle-bisector, RANDOMMATHLOVER, scibeast, ywq233, phoenixfire, rohred1, Jc426, darij grinberg, Filipjack, franzliszt, parmenides51, sub_math, green_leaf, yayups, chrono223, chirita.andrei, a2048, MathInfinite, KST2003, Geo_alphan, Euler01, Aryan27, Mathematicsislovely, math_pi_rate, gatterman, Grizzy, CT17, Mathscienceclass, pi_is_3.14, RodwayWorker, arvind_r, Kayak, DPS, HamstPan38825, SlimTune, Repzram06, CircleGeometryGang, Modesti, Radio2, babygrogu, Matheustxx60, lahmacun, Jahir, mathisawesome2169, SardorNarpay, Math_olympics, EvilRangerGeni, spike2015, ZeusDM, brendan_cape, DarthVader2618, Pitagar, Anant_854, MONYmath10, Vlados021, IvanTea, aourkorzs, Alphatrion, Nymoldin, hi.., amrsan, Critical, alinazarboland, Arhaan, Euler1728, MrOreoJuice, abcbabcba, EpicNumberTheory, BVKRB-, SuperJJ, MathsMadman, cherryolive, sotpidot, N1RAV, bigbrain123, TinTin028, L567, Hamroldt, Nuterrow, a_n, MathsinMaths, Frestho, ChickenAgent2227-_-, gth, SunnySeattle, Math-48, 636510, samrocksnature, Prod55, JVAJVA, ZenTalonsZ, ostriches88, SerdarBozdag, geometrylover123, SP153, Invert_DOG_about_centre_O, mathismyfav2020, aansc1729, e_plus_pi, tigerzhang, judgefan99, AbdulelahAltaf, superagh, MortemEtInteritum, Supermathlet_04, wwn13, menlo, nnathan, vsar0406, miaomiao-, HWenslawski, Tompi2394, hakN, math31415926535, centslordm, Davsch, pieuler, somebodyyouusedtoknow, 554183, bobthefam, bibear, Tnik, DofL, Severus, cadaeibf, SPHS1234, lneis1, Diorite, Flying-Man, ThisUsernameIsTaken, guavaSeabird, math_comb01, Manolis, PhysicsMonster_01, wasikgcrushedbi, oVlad, e61442289, Kdk, IMUKAT, Taco12, Mogmog8, unknown_infinity, megarnie, poppo, JUSTemom, PRMOisTheHardestExam, Seicchi28, roger_dirac, Miku_, Pranav1056, NicoRicci, electrovector, fpccoder, ShiSha, viewsite, asdf334, Khazix, spicemax, aqua2026, eagles2018, HrishiP, Arr0w, Hexagrammum16, NTfish, russellk, AquaFusion04, sargamsujit, Toinfinity, mathking999, fuzimiao2013, yobu, sehgalsh, rayfish, David-Vieta, brandone, Master_of_Aops, EpicBird08, polynomialian, Ritwin, qlip, howcanicreateacccount, resources, peelybonehead, ChromeRaptor777, Amir Hossein, MathWizard10, Sagnik123Biswas, huashiliao2020, ehuseyinyigit, s12d34, Quidditch, Marcus_Zhang, eipilo, aliz, alan9535, sabkx, Ankoganit, Stuffybear, saltamonte, FUNK, rocketsri, SomeonecoolLovesMaths, herbs_li, GreenTea2593, SilverBlaze_SY, amitwa.exe, ATGY, Yrock, Tem8, Tintarn, Funcshun840, ohiorizzler1434, nchuong1312, ROXYYYY, Alex-131, eg4334, Liontiger, MS_asdfgzxcvb, theSpider, cubres, SYBARUPEMULA, CrimsonBlade273, quasar_lord, lightsynth123, lap, CerealCipher, Bata325, nickbaggio
Hey everyone!
I have written a book on Olympiad Number Theory! This book is intended for anyone preparing for their national and international mathematics Olympiads. It covers all the fundamentals, starting from scratch, and moves to almost all the advanced topics you would find in Modern Olympiad problems.
I have taken a very conceptual approach to the subject, and gone into depth of each topic I covered. You can take this book to be a print of how my brain perceives Number Theory
Apart from the theory, I have filled it with handpicked solved examples, some of which are classics, while some are Olympiad problems. The solutions I have discussed are with motivation and would help you develop intuition. The problem section in each chapter starts off easy, and ends at some very challenging albeit beautiful problems. One of my favourite features of this book is the Hints and Solutions system (just like in EGMO) to the problems. Some chapters also have a "special section", which is about an interesting topic related to the chapter, which might even be useful in problem solving. You can read more in the Preface of the book.
This book is my way of giving back to the Olympiad community for the world of knowledge, friends and experience it has given me. I hope you enjoy it
(Published on Academia.edu) Click here to read it. Current Version: V2.
EDIT: Since many people were finding it hard to download the PDF via Academia, here's the drive link. This is Version 2 of the book with (some) typos fixed.
https://drive.google.com/file/d/1BcJTLjQaelZ4w_70oHKyImC2I8zLfyrt/view?usp=sharing
EDIT 2: I am making a list of typos and corrections. Feel free to PM me any typos if you find. I will keep updating the list here: https://drive.google.com/file/d/1xBKFZ7JV4PkYLHCFjZKdXVia0zsd2I_3/view?usp=sharing
EDIT 3: There's a discussion forum for this on AoPS now (wohoo!). Here's the link:
https://artofproblemsolving.com/community/c1610044_modern_olympiad_number_theory
EDIT 4: Here's the old list of typos from the first version: https://drive.google.com/file/d/1C4Z_-utSaJ_Ag1BU9iuzcN9GGN6AHOIv/view?usp=sharing
I have written a book on Olympiad Number Theory! This book is intended for anyone preparing for their national and international mathematics Olympiads. It covers all the fundamentals, starting from scratch, and moves to almost all the advanced topics you would find in Modern Olympiad problems.
I have taken a very conceptual approach to the subject, and gone into depth of each topic I covered. You can take this book to be a print of how my brain perceives Number Theory
Apart from the theory, I have filled it with handpicked solved examples, some of which are classics, while some are Olympiad problems. The solutions I have discussed are with motivation and would help you develop intuition. The problem section in each chapter starts off easy, and ends at some very challenging albeit beautiful problems. One of my favourite features of this book is the Hints and Solutions system (just like in EGMO) to the problems. Some chapters also have a "special section", which is about an interesting topic related to the chapter, which might even be useful in problem solving. You can read more in the Preface of the book.This book is my way of giving back to the Olympiad community for the world of knowledge, friends and experience it has given me. I hope you enjoy it
(Published on Academia.edu) Click here to read it. Current Version: V2.
EDIT: Since many people were finding it hard to download the PDF via Academia, here's the drive link. This is Version 2 of the book with (some) typos fixed.
https://drive.google.com/file/d/1BcJTLjQaelZ4w_70oHKyImC2I8zLfyrt/view?usp=sharing
EDIT 2: I am making a list of typos and corrections. Feel free to PM me any typos if you find. I will keep updating the list here: https://drive.google.com/file/d/1xBKFZ7JV4PkYLHCFjZKdXVia0zsd2I_3/view?usp=sharing
EDIT 3: There's a discussion forum for this on AoPS now (wohoo!). Here's the link:
https://artofproblemsolving.com/community/c1610044_modern_olympiad_number_theory
EDIT 4: Here's the old list of typos from the first version: https://drive.google.com/file/d/1C4Z_-utSaJ_Ag1BU9iuzcN9GGN6AHOIv/view?usp=sharing
This post has been edited 19 times. Last edited by Wizard_32, Mar 14, 2025, 9:29 PM
Reason: Old list of typos
Reason: Old list of typos
for the win 
