An RSA-style trick would be this:

Pick any three digit number you like. Write a 1 after it and then raise it to the 63rd power. Chop off the last digit from the result, and then tell me the last three digits. (For example, if your original number was 712, it would become 7121

^{63}, whose last digits are ...4241

__976__1, and you would tell me 976)

I can now recover your original number by adding back in the final 1 you chopped off, raising it to the 127th power, chopping off the last 1 again, and reporting the last three digits. (For example, 976 becomes 9761

^{127}, whose last digits are ...606129

__712__1, and I would report to you 712)

And there are variants of this for any number of digits, any base, and also allowing different pair of exponents, and even allowing different digits to add and chop off, the latter subject to certain coherence conditions. That's an RSA-style trick.

*But it's not what the trick in post #37 was.*