[throwaway765e6]

For anyone wishing to try this without having to install z3, or just to see a more rudimentary way of doing this, here is a self-contained (hopefully just as readable) solution in JS:

    const num = findNum();
    const bin = num.toString(2);
    const byteStrings = toChunks(bin, 7).map(chunk => chunk.join(''));
    const bytes = byteStrings.map(str => parseInt(str, 2));
    const str = bytes.map(String.fromCharCode).join('');
    console.log(num, bin, byteStrings, bytes, str);
    
    function findNum(i=0, lim=1e1000000000) {
     while (i < lim) {
      if (i % 611939 === 145767 && i % 598463 === 109572) return i;
      i += 1;
     }
    }
    
    function toChunks(iterable, chunkSize) {
     const chunks = [];
     for (const el of iterable) {
      let buf = chunks[chunks.length - 1];
      if (!buf || buf.length >= chunkSize) {
       buf = [];
       chunks.push(buf);
      }
      buf.push(el);
     }
     return chunks;
    }

    243085550 1110011111010011000011101110 [ '1110011', '1110100', '1100001', '1101110' ] [ 115, 116, 97, 110 ] <xxx>

Sorry about not getting a response from the poster of the job, by the way. It's a very unhealthy attitude and it's sad to see this on HN of all places.