questions about the usage of "by"

0Please first see two sets of sentences below:02br
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001. We can solve this problem by using Theorem 20.02br
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002. We can solve this problem using Theorem 20.02br
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00a). The positive integer numbers are also called natural numbers, denoted by N.02br
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00b). The positive integer numbers are also called natural numbers, denoted N.02br
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00You see in 1. and a). the word "by" is used, while in the other sentences, it is omited. My question is: Are they all right? Which are normally used?0-