Question

Show that any positive even integer can be written in the form of 6q, 6q+2, 6q+4, where q is any integer

Answer 1

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Answer 2

Let a be any positive integer

By division algorithm

a = 6q + r, where 0 ≤ r < 6

a = 6q, 6q + 1, 6q + 2, 6q + 3, 6q + 4, 6q + 5

But a is an even integer

a = 6q, 6q + 2, 6q+ 4