2021 JMPSC Sprint Problems/Problem 20
For all integers and , define the operation as Find
Let . Then, and . We substitute these values into expression to get Recall the definition for the operation ; using this, we simplify our expression to We have and , so we can expand the numerator of the fraction within the square root as to get ~samrocksnature
Basically the same as above, but instead we can let . Then we have
which equals .
, , and .
Notice that , substituting this in, we get . Therefore,
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