(38G) x^2+D*y^2=4*p Diophantine Solution
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04-05-2015, 09:07 AM
(This post was last modified: 06-15-2017 01:54 PM by Gene.)
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(38G) x^2+D*y^2=4*p Diophantine Solution
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: |
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