2023 AMC 12B Problems/Problem 7
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Solution
We have
Because is an integer and
is well defined,
must be a positive integer.
Case 1: or
.
The above expression is 0. So these are valid solutions.
Case 2: .
Thus, and
.
To make the above expression real, we must have
.
Thus,
.
Thus,
.
Hence, the number of solutions in this case is 899.
Putting all cases together, the total number of solutions is \boxed{\textbf{(E) 901}}.
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)