“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, ...

ABSTRACT: Here, we determine formulae, for the numbers of representations of a positive integer by certain sextenary quadratic forms whose coefficients are 1, 2, 3 and 6.

Without any structure, DeepMind had to intuit how to solve new equations solely based on seeing a limited number of completed examples. Challenging existing deep learning algorithms with modular math ...

Abstract: Wide-operand modular math functions pose an enormous challenge for verification. We present a novel method to verify a modular reduction engine implemented as a finite state machine (FSM), ...