[seqfan] Re: x(i-1) = ( x(i+1) - x(i)) mod M, period-N solutions?

Ron Hardin rhhardin at att.net
Sun Sep 5 02:08:10 CEST 2010

```It appears that new records are always M^2-1
(-1 since the 0 solution is not counted), except for 4 5 4

>> full current table  occasionally updated at
> > http://rhhardin.home.mindspring.com/current5.txt
> >
> > Ideas,  formulas, is  it already in OEIS in some form...?
>
>
> Records  encoutnered in anti-diagonal order
>
N M #solutions (extended table)
3 2 3
4 5 4
6 4 15
12 8 63
10 11 120
24 12 143
16 21 440
14 29 840
18 38 1443
24 48 2303
20 55 3024
30 62 3843
18 76 5775
48 84 7055
44 89 7920
48 92 8463
48 96 9215
50 101 10200
30 124 15375
24 144 20735
36 152 23103
40 165 27224
48 168 28223
22 199 39600
40 205 42024
42 211 44520
48 224 50175
52 233 54288
48 252 63503
48 276 76175
48 288 82943
36 323 104328
32 329 108240
30 341 116280
28 377 142128
48 414 171395
42 422 178083
40 451 203400
46 461 212520
48 483 233288
26 521 271440
48 552 304703
40 615 378224
60 620 384399
36 646 417315
30 682 465123
72 684 467855
48 736 541695
84 754 568515
70 781 609960
66 796 633615
48 828 685583
42 844 712335
72 856 732735
78 859 737880
80 861 741320
108 872 760383
70 911 829920
72 912 831743
72 918 842723
88 921 848240
48 966 933155
32 987 974168
48 1008 1016063
72 1026 1052675
78 1042 1085763

```