Your opponent uses RSA with $n=pq$ and encryption exponent $e$ and

decrypts a message $m.$ This yields the ciphertext $c=m^e(modn).$ A

spy tells you that, for this message $m^{125}-=1$modn. Explain how can

you find $m.$ Note that you do not know $p,q,(n),$ and you do not

know the secret decryption exponent $d.$ You should find a decryption

exponent that works for this particular ciphertext. Explain carefully

why your decryption works.