MATH10040: Chapter 0 Mathematics, Logic and Reasoning
... Such a number, if it existed, would be a counter-example to Goldbach’s conjecture. (Needless to say, nobody has yet found such a counter-example.) 2.2. Implication. It is important to understand the use of the term implies (the symbol we use for this notion is ‘=⇒’). The following all have the same ...
... Such a number, if it existed, would be a counter-example to Goldbach’s conjecture. (Needless to say, nobody has yet found such a counter-example.) 2.2. Implication. It is important to understand the use of the term implies (the symbol we use for this notion is ‘=⇒’). The following all have the same ...
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[1] presented a deter
... After checking all the 246683 Carmichael numbers < 1016 computed by Pinch [9], we obtain values of the functions f1 (pj ) and f2 (pj ) listed in Table 4. We also find all 566 numbers which are 1-fold Carmichael Sylow pseudoprimes < 1016 . Twenty-three of the 566 numbers are 2-fold Carmichael Sylow ps ...
... After checking all the 246683 Carmichael numbers < 1016 computed by Pinch [9], we obtain values of the functions f1 (pj ) and f2 (pj ) listed in Table 4. We also find all 566 numbers which are 1-fold Carmichael Sylow pseudoprimes < 1016 . Twenty-three of the 566 numbers are 2-fold Carmichael Sylow ps ...
Chapter 1 The Fundamental Theorem of Arithmetic
... Remark: One might ask why we feel the need to justify division with remainder (as above), while accepting, for example, proof by induction. This is not an easy question to answer. Kronecker said, “God gave the integers. The rest is Man’s.” Virtually all number theorists agree with Kronecker in pract ...
... Remark: One might ask why we feel the need to justify division with remainder (as above), while accepting, for example, proof by induction. This is not an easy question to answer. Kronecker said, “God gave the integers. The rest is Man’s.” Virtually all number theorists agree with Kronecker in pract ...
