easy one a)2k+1 = 2m + 4mn + 2n + 1 = (2m+1)(2n+1) so as m,n are positive intergers then (2m+1) and (2n+1) are also intergers ....so clearly 2k+1 is composite b) note that (2k+1) is an odd number . so as it is composite then (2k+1) ....it can be written as product of two odd numbers ...let x and y now x,y are odd so they can be writeen as (2m+1) and (2n+1) for some positive integers m,n so (2k+1) = (2m+1)(2n+1) so k= m+ 2mn + n