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School of Mathematical Sciences
ଜାତୀୟ ବିଜ୍ଞାନ ଶିକ୍ଷା ଏବଂ ଗବେଷଣା ପ୍ରତିଷ୍ଠାନ
राष्ट्रीय विज्ञान शिक्षा एवंअनुसंधान संस्थान
National Institute of Science Education and Research

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Seminar

By bksahoo on Tue, 19/01/2016 - 21:37
Venue
M-4
Speaker
Prof. B. Sury
Affiliation
Indian Statistical Institute, Bangalore
Title
Polynomials, Primes and Progressions

Abstract: Hilbert noted that the polynomial x^4 - 10 x^2 + 1 is irreducible over the integers whereas it is reducible modulo all primes. What is behind this? If two polynomials f,g with integer coefficients take the same set of values modulo all primes, what is the relation between f and g? What proportion of primes divide numbers of the form 2^n + 1? How many of these are of the form 4m+3? What about primes dividing 7^n + 12^n in some arithmetic progression? Are there infinitely many prime numbers such that the decimal expansion of 1/p recurs with period p-1? Given an integer a, if every prime dividing a^n-1 for some n also divides b^n-1, is b necessarily a power of a? We discuss the interesting mathematics behind such questions.

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