Sury B. Number Theory and Combinatorics

Bangalore: Indian Academy of Sciences, 2017. — 186 p.A celebrated mathematician, Prof. Sury’s career has largely been at the Tata Institute of Fundamental Research, Mumbai’, and the Indian Statistical Institute, Bengaluru, where he is presently professor. He has been an important member of the Mathematical Olympiad Program of the country. The present volume brings together some of the writings of B. Sury on Number Theory and Combinatorics which have appeared in ‘Resonance’ journal (which objective is targeted primarily at science education for undergraduate students and teachers) during the last two decades. Each of the articles is a masterpiece ! The book will be valuable to both students and experts as a useful handbook on Number Theory and Combinatorics.Cyclotomy and Cyclotomic Polynomials: The Story of how Gauss Narrowly Missed Becoming a Philologist.
Polynomials with Integer Values.
How Far Apart are Primes ? Bertrand’s Postulate.
Sums of Powers, Bernoulli and the Riemann Zeta function.
Frobenius and His Density Theorem for Primes.
When is a Decimal Expansion Irrational?
Revisiting Kummer’s and Legendre’s Formulae.
Bessels Contain Continued Fractions of Progressions.
The Prime Ordeal.
Extending Given Digits to Make Primes or Perfect Powers.
An Irrational Walk and Why 1 is Not Congruent.
Covering the Integers.
The Story of Two Peerless Indian Mathematicians
Multi-variable Chinese Remainder Theorem.
Which Positive Integers are Interesting?
Counting, Recounting and Matching.
Odd if it isn’t an Even Fit ! Lighting up Tiling.
Polya’s One Theorem with 100 pages of Applications.