Problem: A man born in the first half of the nineteenth century was years old in the year . He was born in:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We seek an integer whose square is between 1800 and 1850 . There is one, and only one, such integer, namely , the year of birth;
or
Let be an integer between 0 and 50 . . For to be integral, the discriminant must be an odd square. The value makes the discriminant . The year of birth is, therefore, .