2002 AMC 10B Problems/Problem 16
Problem
For how many integers is
the square of an integer?
Solution
For the fraction is undefined, for
and
it is negative, hence not a square.
This leaves .
For the fraction equals
, which is a square.
For the fraction is strictly between
and
.
For the fraction equals
, which is a square.
The next square is , and this is achieved for
, and the square after that is
, achieved for
.
That leaves , for which the fraction is
, which is not a square.
In total, there are squares among these fractions.
See Also
2002 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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All AMC 10 Problems and Solutions |