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https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-seed-propagation.htm

The best thing to do at this point will be to wait until it is almost completely dry on top of the soil, down to about 2 inches. Taking too long to dry out is the most common cause of this. Make sure that you can keep the room cool, too.

If they will spot you some peroxide, then a little bit of that mixed in with your water (not exceeding 1/4 the amount of water) and water with this next time, this can combat any diseases setting in.

Most importantly, make sure that there is a way to get rid of any extra water from the watering.

There are many different types of cyclamen, and it would be necessary to know the cultivar to give the best advice on their care.

Here is a link on basic care:https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-care.htm

Here is an article that takes you through the steps to dividing your cyclamen. Follow instructions exactly. You will need a sharp chef's knife if it is large. In pre-internet days, I tried to divide mine and lost both tubers to rot. I hope you have better success; at least you have better information than I did. https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-plant-division.htm

The first thing I would suggest is using a pest control that will be less taxing on the plant's system. Neem oil, rosemary oil, and garlic extract are all really good methods. This collection of articles will help here: https://www.gardeningknowhow.com/special/organic/

And this article will give you information about over-all care of these: https://www.gardeningknowhow.com/houseplants/cyclamen/cyclamen-care.htm

Dear Sir/Madam, I have done it before - cut my cyclamen tuber in half , planted both parts separately and eventually it worked and I had flowers during one year approximately.. my suggestion is , if you really love cyclamens you would go better with seeds, I have seen remarkable results in Internet , ladies have hundreds of them, it takes one year from the start as far as I remember.. you can find further information how to do it , sure.. Hope it helped :)