Question

25 POINTS!

David did not notice the multiplication sign between two three-digit numbers and wrote one six-digit number, which is equal to seven times their product. Find these numbers.


And Also:


Let's call three prime numbers "cool" if their product is five times greater than their sum. How many "cool" triples are there?

Answer 1

The answer to the second problem is 1.

Answer 2

Explanation:

I can only do the first one, and then only by brute force. If both numbers can be the same, then David would write 143143

143 * 143 = 20449

7 * 20449 = 143*143. It is the only answer that came up from 100 to 999.

If I get the second one, I'll put it in the comments. But I can only do it by brute force as well, if I can do it at all.