[Verse 1] Diophantine problems use divisibility Working over Zed means loss of generality [Verse 2] Number rings, the rank of which is finite over Zed Allow for far more factors and put those constraints to bed [Chorus] (We factor, factor!) [Verse 3] Drawback now, our building blocks no longer are unique Enter ideal numbers, that insert a touch of chic [Verse 4] Dedekind domains talk back some sense to number fields Factor each ideal uniquely into prime ideals [Chorus, higher pitch] (Ideals get factored!) [Verse 5] Hitherto the unit group was blissfully ignored For the full arithmetic this need to be restored [Verse 6] Real quadratic fundamental units are devised Pell's equations find solutions parameterized [Chorus, very high pitch] We-fac-tor-num-ber-rings-and-num-ber-fields-and-u-nits-class- group-and-the-like!! Ah-ah-ah...ah-ah...ah-ah! [Climax, end]
