In the history of France between 1700 and 1900, two important victories were recorded on April 22. Let's determine the two years based on the following conditions: a) Exactly 4382 days elapsed between the first and the second victory.

b) The sum of the digits in the year of the first victory is 23.
The time between the two victories is $4382=12 \cdot 365+2$ days, which is 12 years, including two leap years.

According to the Gregorian calendar, which has been in use since 1582, years divisible by 4 are leap years, except for those divisible by 100, unless they are also divisible by 400.

The 12 years can only include two leap years if this period contains a century year. The years 1700 and 1900 are clearly not applicable due to the conditions, so this century year must be 1800. Therefore, the first victory must have occurred between 1788 and 1800.

In this interval, only one number, 1796, satisfies the second condition. Indeed:

On April 22, 1796, Napoleon defeated the Piedmontese forces at Mondovi during the Italian campaign, and on April 22, 1808, he captured Madrid.