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Forum: Miscellaneous Math 2013-08-29, 10:36
Replies: 6
Views: 1,629
Posted By wsc811
Exclamation you can observe the following list

N=4181 as complex
{0,1,0,65}
{1,-44,65,-3}
{2,7,67,19}
{3,-25,66,-5}
{4,-28,59,-4}
{5,-49,53,-2}
{6,-44,45,-2}
{7,-53,43,-2}
{8,-4,63,-32}
Forum: Miscellaneous Math 2013-08-28, 01:33
Replies: 6
Views: 1,629
Posted By wsc811
Or you can use complex number

d = 11 - 4 I; pell = -1; P[0] = 0; Q[0] = 1;
x[0] = (P[0] + Sqrt[d])/Q[0];
a[0] = Round[x[0]];
i = 0;
While[(x[i] != 1/(x[0] - a[0]) && P[i] != pell) || i == 1,
P[i + 1] = Q[i] a[i] - P[i];
...
Forum: Miscellaneous Math 2013-08-28, 01:27
Replies: 6
Views: 1,629
Posted By wsc811
Cool my mathematica code

d = 23*43; pell = -1; P[0] = 0; Q[0] = 1;
x[0] = (P[0] + Sqrt[d])/Q[0];
a[0] = IntegerPart[x[0]];
i = 0;
While[(x[i] != 1/(x[0] - a[0]) && P[i] != pell) || i == 1,
P[i + 1] = Q[i] a[i] - P[i];...
Forum: Miscellaneous Math 2013-08-25, 07:56
Replies: 6
Views: 1,629
Posted By wsc811
Wink why continued fractions gives one factor for N=(4m+3)(4n+3)

for example N=989=23*43 ,Sqrt[N]={a0;a1,a2,...,2a0}
{n,Q,P,a}
{0,1,0,31}
{1,28,31,2}
{2,13,25,4}
{3,20,27,2}
{4,41,13,1}
{5,5,28,11}
{6,52,27,1}
{7,7,25,8}
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