THE CLASS NUMBER OF THE REAL QUADRATIC FIELD Q(?p) AND THE SOLVABILITY OF THE PELL EQUATION x² ­ py² = ±q FOR THE PRIME p = (2q-1)² - 2

It has been obtained a theorem so that the class number to be one of the real quadratic field the type of which the wide Richauct Degert for the p and q primes satisfying 2 2 p = (2q −1) − , ( q ≡/ 3(mod4 ). Finally it has been investigated solvability of the Pell equation q 2 py 2x − = m for the primes p and q.

Keywords:

Class Number, Pell Equation, Principal Forms Chain, Continued Fractions

THE CLASS NUMBER OF THE REAL QUADRATIC FIELD Q(?p) AND THE SOLVABILITY OF THE PELL EQUATION x² ­ py² = ±q FOR THE PRIME p = (2q-1)² - 2

Abstract

THE CLASS NUMBER OF THE REAL QUADRATIC FIELD Q(?p) AND THE SOLVABILITY OF THE PELL EQUATION x² py² = ±q FOR THE PRIME p = (2q-1)² - 2