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SOLVED: Adapt the proof in the text that there are infinitely many primes to prove that there are infinitely many primes of the form 3k 2, where k is a nonnegative integer: [Hint: Suppose that there are only finitely many such primes 41, 42, qn, and consider the number 3q^192 qn 1.]

SOLVED: Adapt the proof in the text that there are infinitely many primes to prove that there are infinitely many primes of the form 3k 2, where k is a nonnegative integer: [Hint: Suppose that there are only finitely many such primes 41, 42, qn, and consider the number 3q^192 qn 1.]

It has been conjectured that there are infinitely many primes of the form n^2-2. Exhibit five such primes. | Numerade

It has been conjectured that there are infinitely many primes of the form n^2-2. Exhibit five such primes. | Numerade

Prove that there are infinitely many primes of the form 2 k p 1, where p is an odd prime. [Hint: Assume that there are finitely many primes of the form 2 k p 1, call them q1, q2, …, qr, and consider the integer .(2 q1 q2 ⋯qr)^p-1 .] | Numerade

Prove that there are infinitely many primes of the form 2 k p 1, where p is an odd prime. [Hint: Assume that there are finitely many primes of the form 2 k p 1, call them q1, q2, …, qr, and consider the integer .(2 q1 q2 ⋯qr)^p-1 .] | Numerade

a prove or disprove there are infinitely many primes of the form 3k 2 where k is a non negative integer 31715

a prove or disprove there are infinitely many primes of the form 3k 2 where k is a non negative integer 31715

Prove that there are infinitely many primes of the form 5 k-1. [Hint: For any n>1, the integer 5(n !)^2-1 has a prime divisor p>n that is not of the form 5 k 1 ; hence, (5 / p)=1 .] | Numerade

Prove that there are infinitely many primes of the form 5 k-1. [Hint: For any n>1, the integer 5(n !)^2-1 has a prime divisor p>n that is not of the form 5 k 1 ; hence, (5 / p)=1 .] | Numerade

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