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Having a Netgear DG834PN router I learned that there is a firmware upgrade available. Having viewed the Netgear site however I was informed ...

"We are sorry to inform that you can't upgrade the firmware from MAC operating system because the firmware file will not be recognized in MAC OS, if you want to upgrade the firmware for the router please upgrade using a Windows based operating system."

So I guess on this issue the score is ... Windoze 1 Mac 0! Grrrrrrrrr

You can upgrade your firmware with your Mac.
My parents have a similar Netgear router (same design, probably slightly different specs) and we've had other Netgear routers before. You can upgrade the firmware in the browser. Indeed, the manual (chapter 5.2) says you can upgrade with your browser. This will work on your Mac, too.

I've upgraded all of my parents routers with their Mac or mine, it has worked every time.

Someone suggested the upgrade might go quicker/better if the downloaded file is put onto a USB memory stick instead of the desktop. Presumably because it is OS neutral. Any views on this?

The firmware upgrade is just a binary blob that you upload to the router through the web interface and it doesn't care what platform you're on. The location you store the firmware image doesn't matter at all.

First, if you don't have the paper manual already, download it here. Read the section in the manual about updating the firmware. Even if the instructions for upgrading the firmware are aimed at a Windows computer, except for some terminology they're really all the same. Below is the basic sketch of how you go about ANY modern router's firmware update. I used the extension Netgear uses, but the process is very generic. If you see a conflict between the manual and what I say below, do what the manual says.

All you have to do is download the "...img" file to some folder you can navigate to (I like using the desktop for this sort of thing). Once it's downloaded, you go into the router's administration pages with your browser, and click the firmware update button. You'll get a pane that lets you select where that ".img" file, so you point it to wherever you downloaded the thing to and select that file. You'll click "OK" or something like that, and the router will read the file and then update its firmware. As long as there is no problem, everything will go fine, the router will reset/restart itself, and all will be well.

I had a Netgear GS108 1Gig switch less than a year old die on me last week. Two capacitors failed. Anyhow, because this is apparently a problem experienced by many people, with bad customer service from Netgear, I will now avoid all Netgear products. What good is a cheap deal if it dies in less than a year. Not so cheap.