(#007) Two proofs in the margin Bharathi Ramana Joshi
Date & Time: 03-10-2020, 22:15 IST
Abstract
Hailed as the queen of mathematics, number theory is one of the most accessible, yet most abstract areas of mathematics. Fermat's Last Theorem, which states that there are no positive integers a, b, c such that a^n + b^n = c^n for any integer value of n > 2, remaind unsolved for 358 years and is the theorem with the largest number of unsuccessful proofs. Although the proof for any n uses heavy machinery from algebraic number theory (indeed, the conjecture drove the development of much of it), the proof for the special case n=4 uses a technique named infinite descent and is accessible. This talk demonstrates application of infinite descent to the n=4 case and two proofs for the same.
Prerequisites
Highschool level understanding of number theory; specifically GCD, pythagorean triples and modular arithmetic (congruence mod n relation).
Resources
None! Just come and enjoy the show