Browsing Pure Mathematics by Subject "mathematics"
Now showing items 1-4 of 4
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Divisibility of Discriminants of Homogeneous Polynomials
(University of Waterloo, 2023-08-28)We prove several square-divisibility results about the discriminant of homogeneous polynomials of arbitrary degree and number of variables, when certain coefficients vanish, and give characterizations for when the discriminant ... -
On a Question of Wintner Concerning the Sequence of Integers Composed of Primes from a Given Set
(University of Waterloo, 2007-09-27)We answer to a Wintner's question concerning the sequence of integers composed of primes from a given set. The results generalize and develop the answer to Wintner’s question due to Tijdeman. -
The Prouhet-Tarry-Escott problem
(University of Waterloo, 2013-01-15)Given natural numbers n and k, with n>k, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of Z, say X={x_1,...,x_n} and Y={y_1,...,y_n}, such that x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. ... -
The Weil conjectures
(University of Waterloo, 2008-01-24)In discussing the question of rational points on algebraic curves, we are usually concerned with ℚ. André Weil looked instead at curves over finite fields; assembling the counts into a function, he discovered that it ...