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 some integer. About the author Mia

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. Reply

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.