Why does some key pair for RSA return same value

[f24u7]

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

 

[Snark1994]

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?