Just to share something I found out, so if you for example divide a point by 35, and then add 1 G to your point and divide the +1 of your point by 35, what do you think will happen?
Well the results of both divisions will have a distance equal of n/35, so if you after dividing p/35, start adding n/35 to your result, for each addition you'd get the result of +1p/35, add n/35 twice, you'd get +2p/35.
Do not fix on EC points, elliptic curve is just "graphical" interpretation of a numbers, all maths behind it works at finite field and obey all laws of "real" numbers math.
If you divide any "real" number by 35, then divide number+1 by 35, then difference between results will be 1/35. This is also works in finite fields and for EC points.
of course if after adding 9 to p, your k ends with 5, then dividing by 5 adding 9/5 won't give you the right key, that's how you can determine what the last digit of your k is.
This is not true, for example - 26/5 = 5,2; 35/5 = 7; 9/5 = 1,8. 26/5+9/5 = 5,2+1,8 = 7 = 35/5
you can also check this with EC points like:
p95 = curve.fromPrivate(9).div(5)
p265 = curve.fromPrivate(26).div(5)
p355 = curve.fromPrivate(35).div(5)
print(p265, p355)
print(p265.add(p95))
output:
03F18D7188F16C93BB251A68DE95A057E02356BA0602854041BA4E170676E54169 025CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC
025CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC