Question

show that every positive odd integer is of the form 6 m + 1 or 6 m + 3 or 6 m + 5 for some integer m
​

Answer 1

Answer:

I thought the answer will be 18

Answer 2

WE CAN SHOW THIS BY USING EUCLIDS DIVISION LEMMA

A=BQ+R(A IS THE ODD INTEGER)

THE POSSIBLE REMAINDER FOR THIS QUESTION IS 0,1,2,3,4,5

FIRST CASE LET THE REMINDER BE 0

SO,

A=6m+0

A=6m

A CANT BE IN THE FORM OF 6m ANYTHING MULTIPLIED BY EVEN NUMBER IS EVEN

A=6m+1

A=6m+1

A IS IN THE FORM OF 6m+1 WHICH GIVES ODD INTEGER

SAME APPLIES WITH THE OTHER REMAINDERS.

BUT ONLY 6m+1,6m+3,6m+5 ARE IN THE FORM OF POSITIVE INTEGERS