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).
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
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).
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).
