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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

NISER

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Seminar

By brundaban.sahu on Tue, 24/05/2016 - 14:46
Venue
Seminar Room, SMS
Speaker
Dr. Prem Prakash Pandey
Affiliation
HRI, Allahabad
Title
Square free values of polynomials

It is conjectured that all separable polynomials with integers coefficients, under some local conditions, take infinitely many (in fact positive density of) square free values on integer arguments. But not a single polynomial of degree greater than $3$ is proven to exhibit this property. We report on some progress towards showing that ``cyclotomic polynomial$\Phi_{\ell}(X)$ take square free values with positive proportion". 

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