Counter-example for an open question regarding Bezout equation check in Solidity.

CoprimalityTest.t.sol

// SPDX-License-Identifier: MIT
// @author Saw-mon and Natalie

pragma solidity 0.8.13;
import "forge-std/Test.sol";

contract CoprimalityTest is Test {

    function verify_coprimality(uint120 a, uint120 b, int x, int y) internal pure {
        unchecked {
            require(int(uint256(a)) * x + int(uint256(b)) * y == 1);
        }
    }

    function testCoprimality() public pure {
        verify_coprimality(
             0xffffffffffffffffffffffffffffe9, // 2 ** 120 - 23
             0xffffffffffffffffffffffffffffe9, // 2 ** 120 - 23
             0x8801832543443c01ef8bdb389ebacc3822c8590b21642c8590b21642c8590b2, // 2 * ( inverse of 2 ** 120 - 23 mod 2 ** 256 )
            -0x4400c192a1a21e00f7c5ed9c4f5d661c11642c8590b21642c8590b21642c859, //   - ( inverse of 2 ** 120 - 23 mod 2 ** 256 )
        );
    }
}