Question

Show that ang positive odd intger is in the form of 4q+1 or 4q+3 where q is some integer

Answer 1

Let a be any positive integer 

by EDL  a = bq +r 

0 ≤ r < b

possible remainders are 0, 1, 2 , 3 

 this shows that a can be in the form of 4q, 4q+1, 4q+2, 4q+3 q is quotient 

as a is odd a  can't be the form of 4q or 4q+2 as they are even

so a ill be in the form of 4q + 1 or 4q+3 

hence proved

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