Learn More
In this paper we give necessary and sufficient trace conditions for an n×n matrix over any commutative and associative ring with unity to be a sum of k-th powers of matrices over that ring, where n, k ≥ 2 are integers. We prove a discriminant criterion for every 2×2 matrix over an order R in an algebraic number field to be a sum of cubes and fourth powers(More)
David R. Richman proved that for n ≥ k ≥ 2 every integral n × n matrix is a sum of seven k-th powers. In this paper, in light of a question proposed earlier by M. Newman for the ring of integers of an algebraic number field, we obtain a discriminant criterion for every n × n matrix (n ≥ k ≥ 2) over an order of an algebraic number field to be a sum of(More)
There was a conference organised at the Institite of Mathematical Sciences, Madras in 1997 on the occasion of the 50th anniversary of India's Independence to review contributions by Indians to various branches of mathematics since Independence. This is a written account of the lecture I gave then on some of the contributions by Indian mathematicians to(More)
Certificate Certified that the summer internship project report " Diophantine Equations " is the bonafide work of " Gaurish Korpal " , Abstract The solution in integers of algebraic equations in more than one unknown with integral coefficients is one of the most difficult problem in the theory of numbers. The most eminent mathematicians like Diophantus (2(More)
  • 1