Question

Show that every positive odd integer is of the form ( 6 m + 1 )or (6m + 3) (6m+ 5)

Answer 1

Answer:

let a be any positive odd integer.

then,by Euclid algorithm

a= 6m+r where 0< r < 6 now,

a=6m+r where r= 0,1,2,3,4

then

a= 6m,6m+1,6m+2,6m+3,6m+4,6m+5.

since 6m, 6m+2 and 6m+4 are even integer .

so (6m+1),(6m+3),(6m+5) are odd integer