Show that any positive odd integer can be written as 6q+1,6q+3, 6q+5 where q is any integer
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Let a is any positive integer, and let b = 6
By applying Eulid's Division Lemma,
we get a = bq + r then the r can be 0 , 1, 2, 3, 4, 5.
Possible values of a = 6q, or 6q+ 1 or 6q+ 2 or 6q + 3 or 6q + 4 or 6q + 5
6q, 6q+2, 6q+4 are divisible by 2.
But 6q+1, 6q+3 or 6q+5 are not divisible by 2.
Hence 6q + 1, 6q + 3 and 6q + 5 are the odd positive inteters
By applying Eulid's Division Lemma,
we get a = bq + r then the r can be 0 , 1, 2, 3, 4, 5.
Possible values of a = 6q, or 6q+ 1 or 6q+ 2 or 6q + 3 or 6q + 4 or 6q + 5
6q, 6q+2, 6q+4 are divisible by 2.
But 6q+1, 6q+3 or 6q+5 are not divisible by 2.
Hence 6q + 1, 6q + 3 and 6q + 5 are the odd positive inteters
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