Not so much interesting problems there, and I'm not allowed to take exams back.
Denote as Legendre symbol.
Def: Order of modulo denoted as is the smallest positive integer such that
Def: be complete residue system modulo .
Def: be reduced residue system modulo .
1.) Find all positive integers such that
- For all , .
2.) Let , be prime numbers. Prove that for all ,
2.1) If , then
2.2) There exists such that and
3.) Let be primes from to inclusively. Find the number of primes such that