Quote from: digaran on September 24, 2023, 09:41:38 PM

Quote from: mcdouglasx on September 24, 2023, 04:04:44 PM

It is difficult to specify which result is integer or not because they are all within the same curve, and can be represented by several pk.

1/2= 57896044618658097711785492504343953926418782139537452191302581570759080747169
3/2= 57896044618658097711785492504343953926418782139537452191302581570759080747170

1/2= 0.5
Secp256k1 curve, 1/2=
57896044618658097711785492504343953926418782139537452191302581570759080747169

3/2= 1.5
Secp256k1 curve, 3/2=
57896044618658097711785492504343953926418782139537452191302581570759080747170

When you operate mod n, 1.5 turns into 0.5+1, or half of n +1. This is true for 1 up to n-1. Like 11/2 is just n/2+5.
So what about 51/2? It's n/2+25, how about 701/2? It's n/2+350. How about 1001/2? It's n/2+500.

Now moving forward, 10001/85= 117.65882
1/85= 0.011764706
Subtracting 0.011764706 - 117.65882 = 117.64706, not integer, now we want to know how to find 0.65882 of n, because 1/85 didn't give us 0.65882, it gives us 0.011764706, but subtracting them gave us some clues, the answer is n.64706th+117. We don't want our result to be a fraction, so we need to find the remainder of division mod n.
Now going bigger, 1000001/85= 11764.718, 1000002/85=
11764.729, 1000003/85= 11764.741, 1000004/85=
11764.753.

See what happened?
0.011764706 1/85
0.011764718 1million and one/85, I added 0.0 - .
0.011764729 1million and two/85, added 0.0 - .
0.011764741 1m and three/85
0.011764753 1m and four/85
If you remove 0.0 from above fractions, you get the correct answer.

51/2 = 25 + 57896044618658097711785492504343953926418782139537452191302581570759080747169

701/2 =350 + 57896044618658097711785492504343953926418782139537452191302581570759080747169

1001/2 =500 + 57896044618658097711785492504343953926418782139537452191302581570759080747169

The results with fractions or float (floating point number) are represented on the curve with integers.

example:

1000001/4 =250000.25

on the curve

86844066927987146567678238756515930889628173209306178286953872356138621370753

publickey

02cdf3e53adf60ad168bccaaed5922ff0a8846de887ca1112bf4a36ae114b32f6b

The longer the fractions, the more difficult it is to calculate their representation in integers on the curve.

It is difficult to know which division is a fraction or not, because the curve sees them as integers.