Use division algorithm to show that any positive odd integer is of the form 6q + 1,

or 6q + 3 or 6q + 5, where q is som

1 thought on “Use division algorithm to show that any positive odd integer is of the form 6q + 1,<br /><br />or 6q + 3 or 6q + 5, where q is som”

1. Step-by-step explanation:

   Let a be a given integer.

   On dividing a by 6 , we get q as the quotient and r as the remainder such that

   a = 6q + r, r = 0,1,2,3,4,5

   when r=0

   a = 6q,even no

   when r=1

   a = 6q + 1, odd no

   when r=2

   a = 6q + 2, even no

   when r = 3

   a=6q + 3,odd no

   when r=4

   a=6q + 4,even no

   when r=5,

   a= 6q + 5 , odd no

   Any positive odd integer is of the form 6q+1,6q+3 or 6q+5.

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