A number-theoretic method using Gaussian integers finds all equal-energy-difference transition pairs in the Bohr model and shows cascades longer than three levels are impossible via Fermat's theorem.
Kantor ,\ @noop title Gray Question 06/00: Hydrogen Atom ( year 2000 a ),\ note https://www.tau.ac.il/ kantor/QUIZ/00/Q06.00.html; accessed May 25, 2026 NoStop
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Transitions with the same energy difference in the Bohr model of the hydrogen atom
A number-theoretic method using Gaussian integers finds all equal-energy-difference transition pairs in the Bohr model and shows cascades longer than three levels are impossible via Fermat's theorem.