Question

Show that any positive odd integer is in the form 4m+1or 4m+3

Answer 1

hello mate here is your answer....
let a be any odd positive integer in a form of
a=bq+r
let r= 0, 1 ,2 ,3
r=0
a=4q+0
=4q
r=1
a=4q+1
r=2
a=4q+2
r=3
a=4q+3
since 4q and 4q + 2 is divisible by 2 and I'm not positive odd integer
therefore, 4q + 1 and 4q + 3 are the odd positive integer.
(here I have taken q instead of m)
HOPE IT HELPS!!!