OFFSET
1,3
COMMENTS
FORMULA
EXAMPLE
The smallest solution to 2*x^2 - p*y^2 = (-1)^((p+1)/4) for the first primes congruent to 3 modulo 4:
n | Equation | x_min | y_min
1 | 2*x^2 - 3*y^2 = -1 | 1 | 1
2 | 2*x^2 - 7*y^2 = +1 | 2 | 1
3 | 2*x^2 - 11*y^2 = -1 | 7 | 3
4 | 2*x^2 - 19*y^2 = -1 | 3 | 1
5 | 2*x^2 - 23*y^2 = +1 | 78 | 23
6 | 2*x^2 - 31*y^2 = +1 | 4 | 1
7 | 2*x^2 - 43*y^2 = -1 | 51 | 11
8 | 2*x^2 - 47*y^2 = +1 | 732 | 151
9 | 2*x^2 - 59*y^2 = -1 | 277 | 51
PROG
(PARI) b(p) = if(isprime(p)&&p%4==3, y=1; while(!issquare((p*y^2 + (-1)^((p+1)/4))/2), y++); y)
forprime(p=3, 250, if(p%4==3, print1(b(p), ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Mar 25 2019
STATUS
approved