A very rich man has given his wife 9,382,481 pearls.
On their engagement he gave her a number of boxes equal to her age in years at that time. In each box were the same number of caskets as there were boxes. In each casket there were the same number of bags as there were caskets. In each bag there were the same number of strings of pearls as there were bags. And on each string there were the same number of pearls as there were strings.
On there wedding day he gave her a second present based on her age in years on her wedding day.
His wife is young, beautiful and was married this year.
How old was she on her engagement and on her wedding day?
If a is her age on engagement and b is her age on her wedding day then a^5 + b^5 must equal 9,382,481.
And a^5 + b^5 = (a + b)(a^4 - a^3 x b + a^2 x b^2- a x b^3 +b^4), so (a + b) is a factor of 9,382,481.
The smallest factor of 9,382,481 is 41, which fits with the wife's age.
We can break 41 down so that a is 20 and b is 21, or a is 19 and b is 22, and so on, and try each of these to see if a^5 + b^5 equals the number of pearls.
If a is 17 then a^5 is 1,419,857 and b is 24 the b^5 is 7,962,624 which add up to the correct number of pearls.
She was 17 when she got engaged and 24 when she married.