Question

show that any positive odd integer is of the form 6q + 1 or 6 Cube + 3 or 6 Cube + 5 Where Q is some integer​

Answer 1

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Answer 2

HERE'S the ANSWER,

Step by Step explanation,
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Let A be any positive odd integers

Therefore, by division algorithm with A and B = 6

Therefore, 0\< r < 6

Therefore, the positive reminders are 0, 1, 2, 3, 4, 5.

Therefore, A can be 6q, 6q + 1, 6q + 2, 6q + 3, 6q + 4, 6q + 5.

Therefore, A is odd and it cannot be divisible by 2

Therefore, A cannot be 6q, 6q + 2, 6q + 4.

Therefore, any positive odd integer is of the form 6q + 1, 6q + 3, 6q + 5.

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