Question

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.


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Answer 1

Clearly, 6q + 1, 6q + 3 and 6q + 5 are of the form 2k + 1, where k is an integer. Therefore, 6q + 1, 6q + 3 and 6q + 5 are not exactly divisible by 2. Hence, these expressions of numbers are odd numbers and therefore any odd integers can be expressed in the form 6q + 1 or 6q + 3 or 6q + 5.

Answer 2

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