Pell's equation: Difference between revisions
→{{header|jq}}
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x = 2,565,007,112,872,132,129,669,406,439,503,954,211,359,492,684,749,762,901,360,167,370,740,763,715,001,557,789,090,674,216,330,243,703,833,040,774,221,628,256,858,633,287,876,949,448,689,668,281,446,637,464,359,482,677,366,420,261,407,112,316,649,010,675,881,349,744,201
y = 27,126,610,172,119,035,540,864,542,981,075,550,089,190,381,938,849,116,323,732,855,930,990,771,728,447,597,698,969,628,164,719,475,714,805,646,913,222,890,277,024,408,337,458,564,351,161,990,641,948,210,581,361,708,373,955,113,191,451,102,494,265,278,824,127,994,180
</pre>
=={{header|jq}}==
{{trans|Wren}}
'''Works with gojq, the Go implementation of jq'''
'''Preliminaries'''
<lang jq># If $j is 0, then an error condition is raised;
# otherwise, assuming infinite-precision integer arithmetic,
# if the input and $j are integers, then the result will be an integer.
def idivide($i; $j):
($i % $j) as $mod
| ($i - $mod) / $j ;
def idivide($j):
idivide(.; $j);
# input should be a non-negative integer for accuracy
# but may be any non-negative finite number
def isqrt:
def irt:
. as $x
| 1 | until(. > $x; . * 4) as $q
| {$q, $x, r: 0}
| until( .q <= 1;
.q |= idivide(4)
| .t = .x - .r - .q
| .r |= idivide(2)
| if .t >= 0
then .x = .t
| .r += .q
else .
end)
| .r ;
if type == "number" and (isinfinite|not) and (isnan|not) and . >= 0
then irt
else "isqrt requires a non-negative integer for accuracy" | error
end ;</lang>
'''The Task'''
<lang jq>def solvePell:
. as $n
| ($n|isqrt) as $x
| { $x,
y : $x,
z : 1,
r : ($x * 2),
v1 : 1,
v2 : 0,
f1 : 0,
f2 : 1 }
| until(.emit;
.y = .r*.z - .y
| .z = idivide($n - .y*.y; .z)
| .r = idivide(.x + .y; .z)
| .v1 as $t
| .v1 = .v2
| .v2 = .r*.v2 + $t
| .f1 as $t
| .f1 = .f2
| .f2 = .r*.f2 + $t
| (.v2 + .x*.f2) as $a
| .f2 as $b
| if ($a*$a - $n*$b*$b == 1) then .emit = [$a, $b] else . end
).emit ;
(61, 109, 181, 277)
| solvePell as $res
| "x² - \(.)y² = 1 for x = \($res[0]) and y = \($res[1])"</lang>
{{out}}
<pre>
x² - 61y² = 1 for x = 1766319049 and y = 226153980
x² - 109y² = 1 for x = 158070671986249 and y = 15140424455100
x² - 181y² = 1 for x = 2469645423824185801 and y = 183567298683461940
x² - 277y² = 1 for x = 159150073798980475849 and y = 9562401173878027020
</pre>
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