Question

show that any postivr odd intrrger is for the form 6q+1

Answer 1

let a and b are two postive no. then there exist two integers q and r
such that a=6q+r
therfore,the possible values of r is 0,1,2,3,4,5
and possible values of a is 6q,6q+1,6q+2,6q+3 ,6q+4 ,6q+5

6q. ,6q+2. ,6q+4 are even positive
integers.
and, 6q+1 ,6q+3 ,6q+5 are odd postive
integers.
hence showed that. 6q+1 is odd postive
integer.