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It happened in 1864

It happened in 1864

A famous mathematician wrote in 1864: "At some point in my life, some years ago, the square of my age coincided with that year."

In what year was the mathematician born?

Solution

If we call n at the age he was in 1864 and we consider that x years before that "moment" took place, then we have that in the year (1864 - x) it would be (n - x) years old and the given condition will be expressed as follows: (n - x)2 = 1864 - x

Since we know that n must be a positive and natural integer the only valid solution is:

Therefore we must find a value close to 1864 whose root is a natural number. The only number before and near 1864 and having a natural root considering a reasonable age, is 1849.
Thus, if we are testing different values ​​of x We find that for x = 15 and n = 58 we get the year 1806.

Thus, the "moment" took place 15 years before 1864 (in 1849) when the mathematician was 58 - 15 = 43 years (43 2 = 1849) so He was born in 1864 - 58 = 1806.