2020 AMC 10B Problems/Problem 9
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Contents
Problem
How many ordered pairs of integers 
satisfy the equation ![\[x^{2020}+y^2=2y?\]](http://latex.artofproblemsolving.com/1/7/5/1757ccd73d86f39d350e40eb82b34f965e4e625c.png)
Solution
Rearranging the terms in the equation gives 
. Completing the square for 
yields the result 
. Then, notice that 
can only be 
, 
and 
because any value of 
that is greater than 1 will cause the term 
to be less than , which is impossible as must be real. Therefore, plugging in the above values for gives the ordered pairs 
, 
, 
, and 
.
Video Solution
See Also
| 2020 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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 10 Problems and Solutions | ||
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