Pell's equation: Difference between revisions
Added Delphi example
(added implementation for Rust) |
MaiconSoft (talk | contribs) (Added Delphi example) |
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Line 283:
x^2 - 181 * y^2 = 1 for x = 2469645423824185801 and y = 183567298683461940
x^2 - 277 * y^2 = 1 for x = 159150073798980475849 and y = 9562401173878027020</pre>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{libheader| Velthuis.BigIntegers}}
{{Trans|Go}}
<lang Delphi>
program Pells_equation;
{$APPTYPE CONSOLE}
uses
System.SysUtils,
Velthuis.BigIntegers;
type
TPellResult = record
x, y: BigInteger;
end;
function SolvePell(nn: UInt64): TPellResult;
var
n, x, y, z, r, e1, e2, f1, t, u, a, b: BigInteger;
begin
n := nn;
x := nn;
x := BigInteger.Sqrt(x);
y := BigInteger(x);
z := BigInteger.One;
r := x shl 1;
e1 := BigInteger.One;
e2 := BigInteger.Zero;
f1 := BigInteger.Zero;
b := BigInteger.One;
while True do
begin
y := (r * z) - y;
z := (n - (y * y)) div z;
r := (x + y) div z;
u := BigInteger(e1);
e1 := BigInteger(e2);
e2 := (r * e2) + u;
u := BigInteger(f1);
f1 := BigInteger(b);
b := r * b + u;
a := e2 + x * b;
t := (a * a) - (n * b * b);
if t = 1 then
begin
with Result do
begin
x := BigInteger(a);
y := BigInteger(b);
end;
Break;
end;
end;
end;
const
ns: TArray<UInt64> = [61, 109, 181, 277];
fmt = 'x^2 - %3d*y^2 = 1 for x = %-21s and y = %s';
begin
for var n in ns do
with SolvePell(n) do
writeln(format(fmt, [n, x.ToString, y.ToString]));
{$IFNDEF UNIX} readln; {$ENDIF}
end.</lang>
=={{header|Factor}}==
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