Question

Show that an integer of the form 6k+5 is also of the form 3k+2, but not conversely

Answer 1

\[6k_0+5 = 6k_0+3+2 = 3(k_0+1)+2=3k_1+2\]
\[k_1,k_2\in Z\]

For a counterexample of the converse
\[2=0*k+2\]but\[2=6x+5\]
has no integer solutions

Answer 2

$$6m+5=3(2m)+3+2=3(2m+1)+2=3n+2$$for \(n=2m+1\) (i.e. odd \(n\)). For even \(n\) in \(3n+2\) we cannot write in the form \(6m+5\).

Answer 3

is there an echo in here? :P

Answer 4

@zzr0ck3r you confused \(k_0,k_1\) and then added some random \(k_2\) afterward

Answer 5

ahh should be k_0,K_1 are in Z