Okay, I know that this is probably super easy. This is not homework, I just grabbed tis book at the library today and am trying to get familiar with the subject (Abstract Algebra). The book is hella old and doesn't have many of the solutions, especially if the author regarded the solution as easy as this (it's the first problem!). My main problem is that I do not know how the proof should look (formally). In the past, I think I recall that a proof must work both ways (forwards and backwards). But I do not know how to start these things. 1. The problem statement, all variables and given/known data An integer [tex]n[/tex] is defined to be even if [tex]n=2m[/tex] for some integer [tex]m[/tex] It is a theorem that the sum of two even integers is even. The definition of an even integer must be used to prove this theorem. 2. Relevant equations [tex]n[/tex] is defined to be even if [tex]n=2m[/tex] 3. The attempt at a solution I don't know where to start..I mean on which side of the equivalency [tex]n=2m[/tex] Should I start like: [tex]n[/tex] is defined to be even if [tex]n=2m[/tex] [tex]n+n=2n=4n[/tex] ....I feel like I am just babbling here....can someone start me off? Thanks, Casey p.s. sorry if this is the wrong forum.