## Why does some key pair for RSA return same value

There are certain key pairs of RSA that will return the same exact value when encrypt and decrypt, for example (5,7) and (13,19)

is there a mathematical pattern that describes this behavior?

Any advice would be appreciated

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 What convention are you using? The only one I've seen is (encoding exponent, modulus), but $2^5 \equiv 4 \pmod 7$ and $2^7 \equiv 3 \pmod 5$, so I presume I have misunderstood your question. Can you give a more specific example?