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Proofreading, while this is on the front page
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LSpice
LSpice
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This could be helpfullhelpful: "Certain other cases of Dirichlet's Theorem have been proved by elementary methods;inmethods; in fact,elementary elementary proofs have been found for general classes..classes…. M. Brauer found a rather simple proof that there are infinitely many primes of the form $ak+1$ and $ak-1$ for every positive integer a"$a$".Topics in the theory of numbers Topics in the theory of numbers by Paul ErdosErdős and Janos Suranyi page 178-180pages 178–180.

This could be helpfull: "Certain other cases of Dirichlet's Theorem have been proved by elementary methods;in fact,elementary proofs have been found for general classes... M Brauer found a rather simple proof that there are infinitely many primes of the form $ak+1$ and $ak-1$ for every positive integer a".Topics in the theory of numbers by Paul Erdos and Janos Suranyi page 178-180.

This could be helpful: "Certain other cases of Dirichlet's Theorem have been proved by elementary methods; in fact, elementary proofs have been found for general classes…. M. Brauer found a rather simple proof that there are infinitely many primes of the form $ak+1$ and $ak-1$ for every positive integer $a$". Topics in the theory of numbers by Paul Erdős and Janos Suranyi pages 178–180.

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Asterios Gkantzounis
Asterios Gkantzounis
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This could be helpfull: "Certain other cases of Dirichlet's Theorem have been proved by elementary methods;in fact,elementary proofs have been found for general classes... M Brauer found a rather simple proof that there are infinitely many primes of the form $ak+1$ and $ak-1$ for every positive integer a".Topics in the theory of numbers by Paul Erdos and Janos Suranyi page 178-180.