seeing more math on the TL recently. i haven't mathposted in a long time but i'm still happy to field math questions from twitter peeps, just reply here or tag me or w/e. big meaty philosophical questions like "wtf are real numbers anyway" would be particularly fun for me rn
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How can I count the numbers of of pairs of adjacent cubes mod prime p? (ie solutions to 1+a^3=b^3 mod p). Why is the answer “write 4p=L^2 + 27M^2; then return p+L-8”? How would I possibly come up with that answer? How should I learn number theory so these questions seem easier?
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these are deep mysteries. you’re right that this is a ludicrously non-obvious answer. a complete answer would involve a description of the relationship between elliptic curves and modular forms and this is stuff that takes multiple years of grad school to understand