Below are a couple of PDF documents on how to resize your images for competitions, in Photoshop and in Faststone Photo Resizer, and a PDF document on how to make your competition entry.
There's also a link to a script for Faststone Photo Resizer. Do note that this script only sets up the image size so you need to set the JPG quality in Settings. I'd recommend setting this to 90%, do not go below 90% because Faststone can be quite aggressive with its compression.
Resizing images with Photoshop
Enhancing Photography Through Collaboration
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