[Verse 1]
When two numbers share a secret code
They're congruent in modular mode
Take any two numbers, call them a and b
If n divides their difference, then they agree
[Chorus]
Same remainder, same remainder
When you divide by n
Congruent means equivalent
In this mathematical den
A congruent b mod n
Three ways to understand
Same remainder when divided
Or n splits their difference grand
[Verse 2]
Let's say we have seventeen and five
With modulus twelve, are they alive
As congruent friends? Let's check it out
Seventeen minus five is twelve, no doubt
[Chorus]
Same remainder, same remainder
When you divide by n
Congruent means equivalent
In this mathematical den
A congruent b mod n
Three ways to understand
Same remainder when divided
Or n splits their difference grand
[Bridge]
Three definitions, all the same
Different windows, same math game
N divides a minus b cleanly
Or remainders match up neatly
Or the difference splits evenly
All three paths lead to the same key
[Verse 3]
Twenty-three and eight mod five
Let's see if congruence comes alive
Twenty-three divided gives remainder three
Eight divided gives remainder three, you see
[Final Chorus]
Same remainder, same remainder
When you divide by n
Congruent means equivalent
In this mathematical den
A congruent b mod n
Now you understand
Same remainder when divided
Makes them congruent, isn't that grand
[Outro]
Modular arithmetic's beautiful way
Same remainders mean they're congruent today