Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6 Cube + 5 Where Q is some integer

Answers (1)

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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