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Generalization of Ruderman's Problem to Imaginary Quadratic Fields
In 1974, H. Ruderman posed the following question: If $(2^m-2^n)|(3^m-3^n)$, then does it follow that $(2^m-2^n)|(x^m-x^n)$ for every integer $x$? This problem is still open. However, in 2011, M. R. Murty and V. K. Murty ...
Smooth Complete Intersections with Positive-Definite Intersection Form
We classify the smooth complete intersections with positive-definite intersection form on their middle cohomology. There are two families. The first family are quadric hypersurfaces in P(4k+1) with k a positive integer. ...