+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Software Libraries (/forum-10.html)
+--- Forum: General Software Library (/forum-13.html)
+--- Thread: (38G) x^2+D*y^2=4*p Diophantine Solution (/thread-3556.html)
(38G) x^2+D*y^2=4*p Diophantine Solution - Gerald H - 04-05-2015 09:07 AM
The programme CORN4 finds the unique integer solution { x, y } of
x ^ 2 + D * y ^ 2 = 4 * p
given 0 < D < 4*p & p prime < 2.5*10^11 or returns 0 if there is no solution..
eg For input
{4563 , 4567}
the programme returns
{4 , 2} in Ans
& indeed
4 ^ 2 + 4563 * 2 ^ 2 = 4 * 4567
The sub-programme SQRTMODP is here
http://www.hpmuseum.org/forum/thread-3448.html
Ans►L1:
Ans(1)►Y:
L1(2)►Z:
IF Ans≥2.5E11
THEN
MSGBOX " π ≥ 2.5E11":
ELSE
IF Z==2
THEN
√(8-Y):
IFTE(FRAC(Ans),0,{Ans,1}):
ELSE
{-Y,Z}:
RUN SQRTMODP:
IF Ans
THEN
ABS((Ans-Y) MOD 2*Z-Ans)►B:
2*Z►A:
INT(2*√Z)►L:
WHILE B>L
REPEAT
A MOD B►R:
B►A:
R►B
END:
√((4*Z-B2)/Y)►C:
IFTE(FRAC(Ans),0,{B,C}):
END:
END:
END: