epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

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Collection of Proofs 121THEOREM 10.by 9,The sum of the cubes of three consecutive integers is divisibleAlleged Proof For the base step observe that 0^ + 1^ + 2^ = 9 is indeeda multiple of 9. Suppose that n^ + (n + 1)^ + (n + 2)^ = 9k for some integernumber fe. Then:(n+l)^+(n + 2)^ + (n + 3)^ = n^+(n+l)^ + (n + 2)^+(n + 3)^-n^= 9/c + 9n^ + 27n + 27= 9(/c + n^ + 3n + 3),which is a multiple of 9.•
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Page 2 and 3:
The Nuts and Bolts of ProofsThird E
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The Nuts and Bolts of ProofsThird E
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List of SymbolsNatural or counting
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List of Symbolsvii(relatively prime
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ContentsList of Symbols vPreface xi
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PrefaceThis book is addressed to th
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Introduction and BasicTerminologyHa
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Introduction and Basic Terminology
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General SuggestionsThe first step,
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Basic Techniques To ProveIf/Then St
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special Kinds of TheoremsThere are
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Special Kinds of Theorems 37Parti.
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Special Kinds of Theorems39Diagram
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Special Kinds of Theorems 41anda <
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Special Kinds of Theorems 43Suppose
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Special Kinds of Theorems 45and^aix
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Special Kinds of Theorems 47EXAMPLE
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Special Kinds of Theorems 493. Usin
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Special Kinds of Theorems 51use the
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Special Kinds of Theorems 53As both
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Special Kinds of Theorems 55Using t
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Special Kinds of Theorems 57If we s
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Special Kinds of Theorems 59B. Ther
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Special Kinds of Theorems 61EXERCIS
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Special Kinds of Theorems 63EXAMPLE
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Special Kinds of Theorems 65If /c >
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Special Kinds of Theorems 67for all
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Special Kinds of Theorems 69conside
Page 84 and 85: Special Kinds of Theorems 71To cons
Page 86 and 87: Special Kinds of Theorems 73We will
Page 88 and 89: Special Kinds of Theorems 75both A
Page 90 and 91: Special Kinds of Theorems 773. Prov
Page 92 and 93: Special Kinds of Theorems 79(For de
Page 94 and 95: Special Kinds of Theorems 81This im
Page 96 and 97: Special Kinds of Theorems 83Let us
Page 98 and 99: Special Kinds of Theorems 85Indeed,
Page 100 and 101: Special Kinds of Theorems 87of the
Page 102 and 103: Special Kinds of Theorems 89where p
Page 104 and 105: Special Kinds of Theorems 91which h
Page 106 and 107: Special Kinds of Theorems 93Thus, w
Page 108 and 109: Special Kinds of Theorems 95The exi
Page 110 and 111: Special Kinds of Theorems 97Thus,\x
Page 112 and 113: Special Kinds of Theorems2n-lpEXAMP
Page 114 and 115: Special Kinds of Theorems 101that l
Page 116 and 117: Review ExercisesDiscuss the truth o
Page 118 and 119: Review Exercises 10519. Let y4 be a
Page 120 and 121: Exercises Without SolutionsDiscuss
Page 122 and 123: Exercises Without Solutions 10922.
Page 124 and 125: Exercises Without Solutions 111(b)
Page 126 and 127: Exercises Without Solutions 113(Thi
Page 128 and 129: Collection of ProofsThe following c
Page 130 and 131: Collection of Proofs 117Alleged Pro
Page 132 and 133: Collection of Proofs 119where k is
Page 136 and 137: Solutions for the Exercises atthe E
Page 138 and 139: Solutions for the Exercises at the
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Solutions for the Exercises at the
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Other Books on theSubject of Proofs
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Other Books on the Subject of Proof
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IndexAlgorithms, Division, 16Argume
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Index 179TTerm, 99Theoremsbasic hyp
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