Bitcoin public key integer arithmetics, help me

[kgpc28]

private key 3 (x = f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9 y = 388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672) divide 2 may output a private key 1? (x = 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 y = 483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)

private key 5 (x = 2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4 y = D8AC222636E5E3D6D4DBA9DDA6C9C426F788271BAB0D6840DCA87D3AA6AC62D6) divide 2 may output a private key 2? (x = C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5 y = 1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A)

private key 11 (x = 774AE7F858A9411E5EF4246B70C65AAC5649980BE5C17891BBEC17895DA008CB y = D984A032EB6B5E190243DD56D7B7B365372DB1E2DFF9D6A8301D74C9C953C61B) divide 10 may output a private key 1? (x = 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 y = 483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)

Can integer arithmetics be used? Not modular arithmetics.

[j2002ba2]

There cannot be integer arithmetic for secp256k1 curve, since it has no solutions in integer or rational numbers. The integer solutions of any elliptic curve are limited number, usually quite low one. There is no upper bound of that number, since you could multiply the coordinates and d by very very large numbers, thus removing denominators.

There are isomorphic curves, in which you could go with rational numbers, curves in the form of y² = x³ + d, which can be obtained by multiplying by t: (y*t³)² = (x*t²)³ + 7*t⁶. The smallest positive integer d for curve of rank 1 is 12, the smallest in absolute value is -2. Of course the coordinates grow very very big, very very fast. As an exercise you could find out (x,y) mod p coordinates for d=12 by moving the point to (x*t², y*t³), t=1806032470229063221237645096224748984265920240071041634471134158090974399836, one of the six possible values for sixthroot(12/7) mod p. Then the smallest x numerator of rational coordinate producing it has maximum number of bits ~2⁵¹², y numerator ~2⁷⁶⁸, and both have a denominator in the form of z² for x, and z³ for y, z having max ~2²⁵⁶ bits.

If you use y² = x³ + 12, with generator (-2,2) then you'd get the following coordinates:
1: (-2 2)
2: (13 -47)
3: (-74/225 11674/3375)
5: (14932678/8994001 109819305542/26973008999)
11: (261861850180472271248849532094782118/4756672475309420795224474860473521
 -134005914121975045481665034854476269198005341316588858/328061202989677115836137338038693498061075340702569)