ALGORITHMIC NUMBER THEORY

By Q. RAMIK

CONTENTS I LECTURES 1 LECTURE-WISE BREAK UP 2 DIVISIBILITY AND THE EUCLIDEAN ALGORITHM 3 FIBONACCI NUMBERS 4 CONTINUED FRACTIONS 5 SIMPLE INFINITE CONTINUED FRACTION 6 RATIONAL APPROXIMATION OF IRRATIONALS 7 QUADRATIC IRRATIONAL(PERIODIC CONTINUED FRACTION) 8 PRIMES AND THER INFINITUDE 9 TCHEBYCHEV’S THEOREM 10 LINEAR CONGRUENCES, CHINESE REMAINDER THEOREM AND FERMAT’S LITTLE THEOREM 11 EULER’S ? FUNCTION, GENERALISATION OF FLT, CRT 12 CONGRUNCES OF HIGHER DEGREE 13 LAGRANGE’S THEOREM 14 PRIMITIVE ROOTS AND EULER’S CRITERION 15 QUADRATIC RECIPROCITY 16 APPLICATIONS OF QUADRATIC RECIPROCITY 17 THE JACOBI SYMBOL 18 ELEMENTARY ALGEBRAIC CONCEPTS 19 SYLOW’S THEOREM 20 FINITE ABELIAN GROUPS & DIRICHLET CHARACTERS 21 DIRICHLET PRODUCTS 22 PRIMES ARE IN P II EXAMPLES 23 AKSHAT VERMA 24 RAHUL GUPTA 25 GAURAV GUPTA 26 ASHISH RASTOGI 27 DHAN MAHESH 28 MAYANK KUMAR 29 HITESH CHAUDHARY 30 SATISH PARVATANENI 31 BIPIN TRIPATHI 32 AMIT AGARWAL 33 VIPUL JAIN 34 TUSHAR CHAUDHARY 35 KESHAV KUNAL 36 AKROSH GANDHI 37 SAI PRAMOD KUMAR 38 TARIQ AFTAB 39 VIKAS BANSAL 40 ANUJ SAXENA