LECT # 4|| CH# 2 THEORY OF PRIMES|| PROOF OF τ(n)=NUMBER OF DIVISORS|| σ(n)=SUM OF DIVISORS FORMULAS скачать в хорошем качестве

LECT # 4|| CH# 2 THEORY OF PRIMES|| PROOF OF τ(n)=NUMBER OF DIVISORS|| σ(n)=SUM OF DIVISORS FORMULAS

This course is specially designed for students of B.S MATHEMATICS 4th semester of Punjab university Lahore Pakistan. ------------------------------------------------------------------------------------------------------------------------------------------------------- COURSE: ELEMENTARY NUMBER THEORY||PUNJAB UNIVERSITY|| 4TH SEMESTER|| CODE 206 LEVEL: B.S MATHEMATICS CHAPTER # 2 THEORY OF PRIMES LECTURE # 4 PROOF OF τ(n)=NUMBER OF DIVISORS|| σ(n)=SUM OF DIVISORS FORMULAS ------------------------------------------------------------------------------------------------------------------------------------------------------- In this lecture I shall prove two important formulas one is related to find number of positive divisors of an integer n and other is related to find sum of all positive divisors of n. ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH COMPLETE PLAY LIST OF NUMBER THEORY CLICK THE LINK BELOW    • NUMBER THEORY by Professor Azmat Ali || BS...   ------------------------------------------------------------------------------------------------------------------------------------------------------- COURSE CONTENTS In this play list you can find the following contents (1) L.C.M & H.C.F (2) TESTS OF DIVISIBLITY (3) STATEMENT AND PROOF OF EUCLID THEOREM OF DIVISIBLITY. (4) THEOREM ON PROPERTIES OF DIVISIBILTY (5) THEOREM ON L.C.M AND H.C.F (6) LINEAR DIOPHANTINE EQUATION. (7) NECESSARY AND SUFFICIENT CONDITION OF LINEAR DIOPHANTINE EQUATION TO BE SOLVABLE. (8) PROBLEMS RELATED TO MATHEMATICAL INDUCTION. (9) PENTAGONAL NUMBER. (10 ) HOW TO FIND DAY OF THE WEEK. (12) CONGRUENCY (13) PROPERTIES OF CONGRUENCY (14) THEOREM ON CONGRUENCE (15) HOW TO FIND REMAINDER OF THE NUMBER BY USING CONGRUENCE RELATION. (16) SOLUTION OF LINEAR CONGRUENCE (17) CHINESE REMAINDER THEOREM (18) PROBLEMS RELATED TO CHINESE REMAINDER THEOREM. (19) EUCLID THEOREM (20) THE SIEVE OF ERATOSTHENES. (21) PERFECT NUMBER, MERSENNE PRIMES, FERMAT NUMBERS. (22) THEOREM RELATED TO PRIME NUMBERS (23) MODULAR ARITHMETIC (24) THEORY OF PRIMES (25) ARITHMATICAL FUNCTIONS (26) MULTIPLICATIVE FUNCTIONS (27) CONGRUENCES POLYNOMIAL (28) FACTOR THEOREM (29) LAGRANGE'S THEOREM (30) WILSON THEOREM (31) SOLUTION OF POLYNOMIAL CONGRUENCES (32) EULER FUNCTION (33) EQUIVALENCE CLASS (34) CONGRUENCE CLASS (35) COMPLETE RESIDUE SYSTEM (36) EULER PHI FUNCTION (37) REDUCED RESIDUE SYSTEM (38) FERMAT LITTLE THEOREM ------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------- My lectures have equal importance for students of all universities of Pakistan, India, Bangladesh and all other countries where universities are offering this course. Specially my lecture may be very helpful for students of following universities of Pakistan (1) LAHORE UNIVERISTY (2) PUNJAB UNIVERISTY (3) SARGODHA UNIVERISTY (4) FAST UNIVERISTY (5) VIRTUAL UNIVERISTY (6) BZU(BHAU DIN ZIKRIYA) UNIVERISTY (7) G.C UNIVERISTY (8) F.C COLLEGE UNIVERSITY (9) U.E.T (10) GUJRAT UNIVERSITY (11) PISHAWAR UNIVERSITY (12) SINDH UNIVERSITY (13) COMSAT (14) LUMS UNIVERSITY ------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------- THIS VIDEO MAY BE HELPFUL FOR PAKISTANIS, INDIAN, BANGLADESIAN AND ALL THE MATHEMATICS STUEDENTS OF THE WORLS WHO KNOWN URDU LANGUAGE WELL. ------------------------------------------------------------------------------------------------------------------------------------------------------- Share, Support, Subscribe!!! About: Maths 4 U is a You Tube Channel, where you can learn Mathematics in very simple way. In this channel you can find Mathematics Videos for Intermediate and B.S Mathematics. Further in my channel you can find videos for following Entrance Exams (1) ECAT (2) CSIR (3)GATE (4) NET (5) JEE MAIN (6) JEE ADVANCED (7) IIT-JEE (8) AIEEE, DCE (9) EAMCET, WB -JEE (10) ORISSA JEE & BIHAR CET (11) MP & RAJASTHAN PET (12) KERALA PET (13) PUNJAB & HARYANA CET & OTHER ENGG. INSTITUITES Here you can find Challenging Math's Problems related to daily life. Further you can find MATHS videos for the preparation of COMPETITIVE EXAMS like as CSS, PMS and PPSC. Here you can also find lectures on use of some Mathematics software's like as Math Type, LaTex, Matlab and Mathematica. #Maths4U. #professorazmatali #divisors