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.)(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# How to formalize

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