# Show that every positive odd integer are in the form of 7q + 1,7q + 2,7q+ 3,7q + 4,7q + 5,7q+ 6?please tell the answer...

SOLUTION :     Let a be any odd positive integer and  b = 7  By division  Lemma there exists integers q and r such that

$\\ a=7q+r , \\ \Rightarrow 0\leq r< 7$

⇒  a = 7q  or , a =7q+1 or , a =7q + 2 or, a=7q+3 or, a=7q+4 or, a =7q+5 or , a =7q +6    ⇒( r = 0,1,2 ,3 ,4 ,5 ,6 )

⇒ Hence, any odd integer is of the form  7q+1 ,7q+2 ,7q+3 , 7q+4 ,7q+5 ,7q+6

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