Igor saw Pavel at a mathematics conference.

“Pavel!” he exclaimed. “How are you? How are your two children? I don't remember their ages, but I recall when I saw you last, their ages had the curious property that the sum was a multiple of the difference.”

“That's true again,” replied Pavel. “But this year, the product of their ages is also a multiple of the sum.”

How long has it been since Igor saw Pavel? What are the ages of Pavel's children now?