Unformatted text preview: 1.2.31: Let n ≥ 2 and k be any positive integers, Prove that ( n1)  ( n k1) . Exercise 4. 1.2.32: Let n ≥ 2 and k be any positive integers, Prove that ( n1) 2  ( n k1) if and only if ( n1)  k . Exercise 5. 1.3.24: Show that n ≥ 2 has a prime factor p ≤ √ n if n is composite. Exercise 6. 1.3.36: Let S be the set of integers 1 , 2 , 3 , . . . , n and let 2 k be the highest power of 2 within S . Prove that 2 k does not divide any other element of S . Deduce that ∑ n i =1 1 i is not an integer for n ≥ 2....
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 Spring '08
 Humphreys,G
 Prime number, Greatest common divisor, positive integers, ﬁve lowest scores

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