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Maplesoft Document System Sat, 13 Jun 2026 18:43:34 GMT Sat, 13 Jun 2026 18:43:34 GMT The latest answers and comments added to the Question, Pell's Equation - how to check solutions in Maple? http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions?ref=Feed:MaplePrimes:Pell's Equation - how to check solutions in Maple?:Comments#answer102588 <p>Look at&nbsp; the <a href="http://www.maplesoft.com/support/help/search.aspx?term=isolve">?isolve</a> command.</p> <p>&gt;isolve(x^2-29*y^2=1);</p> <p>PS.</p> <p>&gt; simplify(eval({x = -(1/2)*(9801+1820*sqrt(29))^_Z1-(1/2)*(9801-1820*sqrt(29))^_Z1, y = -(1/58)*sqrt(29)*((9801+1820*sqrt(29))^_Z1-(9801-1820*sqrt(29))^_Z1)}, _Z1 = 2));</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {x = -192119201, y = -35675640}</p> <p>Look at&nbsp; the <a href="http://www.maplesoft.com/support/help/search.aspx?term=isolve">?isolve</a> command.</p> <p>&gt;isolve(x^2-29*y^2=1);</p> <p>PS.</p> <p>&gt; simplify(eval({x = -(1/2)*(9801+1820*sqrt(29))^_Z1-(1/2)*(9801-1820*sqrt(29))^_Z1, y = -(1/58)*sqrt(29)*((9801+1820*sqrt(29))^_Z1-(9801-1820*sqrt(29))^_Z1)}, _Z1 = 2));</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {x = -192119201, y = -35675640}</p> 102588 Thu, 17 Mar 2011 10:13:58 Z hirnyk hirnyk http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions?ref=Feed:MaplePrimes:Pell's Equation - how to check solutions in Maple?:Comments#answer102596 <p>Ten solutions by <a href="http://www.maplesoft.com/applications/view.aspx?SID=101333">DirectSearch package</a>:</p> <p>with(DirectSearch):<br>SolveEquations(x^2-29*y^2=1, tolerances=10^(-14), AllSolutions, solutions=10);</p> <p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=3606b7f7a1af4f119a31a55a1cccbb53.gif" alt="Matrix(10, 4, {(1, 1) = 0., (1, 2) = Vector(1, {(1) = 0.}), (1, 3) = [x = 1.500840386291, y = -.207823023609373], (1, 4) = 275, (2, 1) = 0., (2, 2) = Vector(1, {(1) = 0.}), (2, 3) = [x = -37.8326124564575, y = 7.02288516524052], (2, 4) = 327, (3, 1) = 0., (3, 2) = Vector(1, {(1) = 0.}), (3, 3) = [x = -13.6095592135261, y = -2.52040022811426], (3, 4) = 224, (4, 1) = 0., (4, 2) = Vector(1, {(1) = 0.}), (4, 3) = [x = 2.55906305386593, y = .437422060591118], (4, 4) = 323, (5, 1) = 0., (5, 2) = Vector(1, {(1) = 0.}), (5, 3) = [x = -84.7731137700263, y = 15.7408767427312], (5, 4) = 261, (6, 1) = 0., (6, 2) = Vector(1, {(1) = 0.}), (6, 3) = [x = -96.9858983459182, y = -18.0088718346654], (6, 4) = 285, (7, 1) = 0., (7, 2) = Vector(1, {(1) = 0.}), (7, 3) = [x = 90.0007814048697, y = 16.7116938755236], (7, 4) = 259, (8, 1) = 0., (8, 2) = Vector(1, {(1) = 0.}), (8, 3) = [x = 45.8002609373078, y = -8.50286747155392], (8, 4) = 249, (9, 1) = 0., (9, 2) = Vector(1, {(1) = 0.}), (9, 3) = [x = -1.00040339992736, y = 0.527506360875102e-2], (9, 4) = 261, (10, 1) = 0., (10, 2) = Vector(1, {(1) = 0.}), (10, 3) = [x = -51.7069917328136, y = -9.59995149782513], (10, 4) = 258})"></p> <p>Ten solutions by <a href="http://www.maplesoft.com/applications/view.aspx?SID=101333">DirectSearch package</a>:</p> <p>with(DirectSearch):<br>SolveEquations(x^2-29*y^2=1, tolerances=10^(-14), AllSolutions, solutions=10);</p> <p><img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=3606b7f7a1af4f119a31a55a1cccbb53.gif" alt="Matrix(10, 4, {(1, 1) = 0., (1, 2) = Vector(1, {(1) = 0.}), (1, 3) = [x = 1.500840386291, y = -.207823023609373], (1, 4) = 275, (2, 1) = 0., (2, 2) = Vector(1, {(1) = 0.}), (2, 3) = [x = -37.8326124564575, y = 7.02288516524052], (2, 4) = 327, (3, 1) = 0., (3, 2) = Vector(1, {(1) = 0.}), (3, 3) = [x = -13.6095592135261, y = -2.52040022811426], (3, 4) = 224, (4, 1) = 0., (4, 2) = Vector(1, {(1) = 0.}), (4, 3) = [x = 2.55906305386593, y = .437422060591118], (4, 4) = 323, (5, 1) = 0., (5, 2) = Vector(1, {(1) = 0.}), (5, 3) = [x = -84.7731137700263, y = 15.7408767427312], (5, 4) = 261, (6, 1) = 0., (6, 2) = Vector(1, {(1) = 0.}), (6, 3) = [x = -96.9858983459182, y = -18.0088718346654], (6, 4) = 285, (7, 1) = 0., (7, 2) = Vector(1, {(1) = 0.}), (7, 3) = [x = 90.0007814048697, y = 16.7116938755236], (7, 4) = 259, (8, 1) = 0., (8, 2) = Vector(1, {(1) = 0.}), (8, 3) = [x = 45.8002609373078, y = -8.50286747155392], (8, 4) = 249, (9, 1) = 0., (9, 2) = Vector(1, {(1) = 0.}), (9, 3) = [x = -1.00040339992736, y = 0.527506360875102e-2], (9, 4) = 261, (10, 1) = 0., (10, 2) = Vector(1, {(1) = 0.}), (10, 3) = [x = -51.7069917328136, y = -9.59995149782513], (10, 4) = 258})"></p> 102596 Thu, 17 Mar 2011 16:56:29 Z mois mois http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions?ref=Feed:MaplePrimes:Pell's Equation - how to check solutions in Maple?:Comments#answer102665 <p>thank you for your help! antonio</p> <p>thank you for your help! antonio</p> 102665 Sun, 20 Mar 2011 14:40:44 Z Antonio_S Antonio_S http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions?ref=Feed:MaplePrimes:Pell's Equation - how to check solutions in Maple?:Comments#answer102666 <p>thank you for your help! antonio</p> <p>thank you for your help! antonio</p> 102666 Sun, 20 Mar 2011 14:40:49 Z Antonio_S Antonio_S http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions?ref=Feed:MaplePrimes:Pell's Equation - how to check solutions in Maple?:Comments#comment102607 <p>The solutions of Pell's equation are assumed to be integer numbers.</p> <p>The solutions of Pell's equation are assumed to be integer numbers.</p> 102607 Thu, 17 Mar 2011 19:51:50 Z hirnyk hirnyk http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions?ref=Feed:MaplePrimes:Pell's Equation - how to check solutions in Maple?:Comments#comment102617 <p><a href="http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions#comment102607">@hirnyk</a> For integer solution your proposal to use isolve command is optimal.</p> <p><a href="http://www.mapleprimes.com/questions/102585-Pells-Equation--How-To-Check-Solutions#comment102607">@hirnyk</a> For integer solution your proposal to use isolve command is optimal.</p> 102617 Thu, 17 Mar 2011 21:10:26 Z mois mois