The Mathematician’s Kids

A mathematician named Albert meets a colleague and says: “Nice to see you again John. How is life?”

“I am prosperous, Albert, and happily married with three kids.”

“That’s nice. How old are they?” asked Albert.

“The product of their ages is 36 and the sum is equal to the number of swans you can see in my private lake,” pointing out the window.

Albert thought for a while, then he said. “That’s not enough information, John”

“You are right, I forgot to tell you that the age sum divides that of their squares,” replied John.

Albert thought for a while, smiled and said: “Ok, now I know how old they are, John”

How old are the kids and how many swans are in the private lake?

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