2023 AMC 12B Problems/Problem 7
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)
See Also
2023 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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