Wednesday, 21 May 2014

Ramanujan-Nagell theorem

A very interesting Diophantine equation problem was conjectured in 1913 by Srinivasa Ramanujan and proved in 1948 by Trygve Nagell.  The Ramanujan-Nagell theorem states that the only positive integer solutions of the equation

x 2 + 7 = 2 y

are (1,3), (3,4), (5,5), (11,7) and (181,15).  It can be proved by using the uniqueness of factorization in the ring of integers of the quadratic field Q(√-7).

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