CBSE Class 10 Answered

I CASE

let x be any no. divided by 6

x=6q,6q+1,6q+2,6q+3,6q+4,6q+5

considering x=6q+5

x=6q+5

 =6q+3+2

=3(2q+1)+2

let 2q+1 be m

x=3m+2

thus 6q+5 can be expressed in form of 3q+2.(3m+2)

II CASE

let x be any no. divided by 3

x=3q,3q+1,3q+2

when x=3q+2

=3q+2

even if we multiply it by 2 or 3 we get x=6q+4,or x=9q+6

in noway can we get x=6q+5.

hence proved that if any positive integer is of form 6q+5,then it is of form 3q+2 for some positive integer q,but not conversely.