Sophie Germain Primes
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Hello,
I need help with proving the following statement:
"A prime p is said to be a Sophie Germain prime if n = 2p+1 is also prime.
Prove that a prime p is a Sophie Germain prime if and only if 2^(n-1) = 1 (mod n)."
Thank you for your time.
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Solution Summary
The solution examines if Sophie Germain is prime.
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Proof:
" ": If the prime is a Sophie Germain prime, then is also prime. Obviously we have , according to Fermat's Little Theorem, we have
(mod )
" ": If , is a prime and we have (mod ), we want to show that is a prime. It is obvious that , according to Euler's Totient Theorem, we ...
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