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Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.

2 votes
0 answers
198 views

Reciprocity theorem with $n \ge 5$

If $p \equiv 1 \pmod n$, what additional conditions are needed to ensure that $$2^{(p-1)/n} \equiv 1 \pmod p?$$ I know: For $n=3$ (cubic reciprocity) the form is $p=x^2+27y^2$. For $n=4$ (biquadra …
zomega's user avatar
  • 131
1 vote
0 answers
81 views

Which prime numbers fit into my equation similiar to Fermat's little theorem? [closed]

Fermat's little theorem says: $a^{p-1} \equiv 1 \pmod p$ I have a equation which is similar to this but it's not covered by Fermat's theorem nor by Euler's theorem. My equation is: $2^{(p-1)/3} \e …
zomega's user avatar
  • 131