Question

show that any positive odd integer is in the form of 6q+1, 6q+3 or 6q+5where q is some integer

Answer 1

Answer:

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.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Let 'a'be any positive integer and 'b'be 6

on dividing a by b we get

a=bq+r (where q is quotient and r is remainder)

=>a=6q+r

r may have the value of 0,1,2,3,4,5

when r=0

a=6q+r=6q(even)

when r=1

a=6q+r (odd)

when r =2

a=6q+2 (even)

when r=3

a=6q+3 (odd)

when r=4

a=6q+4 (even)

when r=5

a=6q+5 (odd)

Now we can clearly see that which equations are odd

Hence, Any positive odd integer is of the form

6q+1 , 6q+3 and 6q+5

Hope this will help u

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