[Verse 1]
Two primes meet at a mathematical soirée
Seven asks thirteen, "Am I a perfect square your way?"
Thirteen whispers back, "You're residue in my domain"
But there's a secret deeper than this number game
[Chorus]
It's the secret handshake, quadratic reciprocity
If p sees q, then q sees p with symmetry
When both are three mod four, flip the sign around
Gauss discovered structure where chaos once was found
Secret handshake, secret handshake
Hidden patterns that the primes all make
[Verse 2]
Like strangers at a party who discover they've been
At all the same gatherings, a network unforeseen
The Legendre symbols dance in perfect harmony
What you are to me, I am to you with one key
[Chorus]
It's the secret handshake, quadratic reciprocity
If p sees q, then q sees p with symmetry
When both are three mod four, flip the sign around
Gauss discovered structure where chaos once was found
Secret handshake, secret handshake
Hidden patterns that the primes all make
[Bridge]
p over q equals q over p
Unless they both leave three when divided by four
Then multiply by minus one and see
The reciprocal relationship core
[Verse 3]
From seemingly random residues emerged a law
Connecting distant primes through what young Gauss saw
A theorem of connection where none should exist
The mathematical handshake that can't be missed
[Chorus]
It's the secret handshake, quadratic reciprocity
If p sees q, then q sees p with symmetry
When both are three mod four, flip the sign around
Gauss discovered structure where chaos once was found
Secret handshake, secret handshake
Hidden patterns that the primes all make
[Outro]
In the realm of number theory's grand design
Every prime knows every other's quadratic sign