Question

2. Show that any positive odd integer is of the form ( 6m + 1 ), ( 6m + 3 ) or ( 6m ,+ 5 )

Class 10

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Answer 1

♥️Hi there ♥️

Let a be any odd positive integer and b = 6 .Then there are exist integers q and r such that .

By eucild division Lemma,

$a = 6q + r$
$0 \leqslant r < 6$

a can be 6q ,6q +1 , 6q +2 , 6q+3 , 6q +4 or 6q+5 .

But 6q , 6q +2 , 6q +4 are even +pos integers .

a= 6q+1 , 6q+3 and 6q+5.

Thanks !