Why does some key pair for RSA return same value

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The discussion centers on the phenomenon where certain RSA key pairs, specifically (5,7) and (13,19), yield identical values during encryption and decryption processes. Participants explore the mathematical patterns that may explain this behavior, questioning the conventions used in RSA encryption, particularly the encoding of the exponent and modulus. The conversation highlights the need for clarity in examples to better understand the underlying principles of RSA key generation and its implications.

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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?
 

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