by James Hamblin Smith's A treatise on elementary algebra PDF

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X p1

The theorem follows. p a twin prime p X Homework: (1) Let pn denote the nth prime. (a) Explain why the Prime Number Theorem implies that lim sup(pn+1 ? pn ) = 1. 1 (b) Use Theorem 43 to prove that for every positive integer k, ? lim sup minfpn+1 ? pn ; pn+2 ? pn+1 ; : : : ; pn+k ?

C) Justify the rst comment made after the statement of Theorem 41. (2) (a) For z > 1, de ne (n) = 1 ? X p z p 3 (mod 4) pjn 1+ X p1

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A treatise on elementary algebra by by James Hamblin Smith

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