[seqfan] number-theoretic notation

[Ed Jeffery]

I have been studying an obscure article that, in part, enumerates certain
classes of subfields, and I want to eventually submit the sequences if they
are not in OEIS. However, in studying their equations, I noticed that the
authors used the notation

p | m,

which I take to mean the usual the "prime p divides m" (or with a slash
through the line to mean the converse), but several times in conjunction
with that, and often in the same paragraph or sentence, they use the
notation

p || m.

The two vertical lines I have never seen before as a binary relation in
number theory. I checked my Hardy & Wright, 5th ed., as well as my old
Harper Collins mathematics dictionary, and did not find this, and I have
been searching online all day with no luck. Note that in the article, p
always denotes a prime, and m is a positive integer.

Does anyone know what that notation means in the number-theoretic context?