I increasingly find demonstrations in number theory that rely on verbal arguments, rather than a more algebraic proof involving notation. (I hope this is just my fault.) For example, consider this simple statement, "If n divides a.b but does not divide a or b individually, then n is composite and can be expressed as n = r.s, where r|a and s|b." In order to prove it, I have to proceed like this: a prime factor in n must appear in either a or b; were n prime, if would divide either a or b. Thus it is composite, and made of prime factors coming from either a or b." Sort of. Is there a way of not having to talk? Some formalism for this? (I hope so.) Otherwise I'd find number theory a bit lacking. Opinions welcome.