Show that any positive odd integer is of the form `6q+1` or `6q+3` or `6q+5`, where `q` is some integer
Text Solution
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Let `a` and `b` are two positive integers such that `a>b`.
then, for any integer `q`, we can write,
`a = bq+r`, where r is remainder if we divide `a` by `b`.
If, `b=6`,then,
`a = 6q+r`
Now, for any positive odd integers, `r` can be `1` or `3` or `5`.
So,
`a = 6q+1` or `a= 6q+3` or `a = 6q+5`
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