Does elementary number theory have any applications in physics? If so how?
quantum computing, quantum information theory (well, stictly speaking, that's just information theory but it is hot topics in physics right now)
There's a lot of overlap between number theory and symmetry, which is pretty central to Physics. There's a book called "Why Beauty is Truth" by Ian Stewart that traces the development of number theory and its various off-shoots with an eye to symmetry and how it applies in Physics. I recommend it to anyone interested in such things.
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