YOU KNOW THE DRILL 2.0
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If 
is odd, then
while if is even, then the sum would be
The latter case is easier to solve:
which means
.
In the odd case, instead of considering the above equation we can consider the partial sums. If is odd, then the sum of the even integers between 1 and would be
Now consider the partial sum up to the second-to-last term,
Subtracting this from the previous partial sum, we have
We're given that the sums must add to
, which means
But taking the differences now yields
and there is only one for which 
; namely, 
. However, the sum of the even integers between 1 and 5 is 
, whereas 
. So there are no solutions to this over the odd integers.
while if
The latter case is easier to solve:
which means
In the odd case, instead of considering the above equation we can consider the partial sums. If
Now consider the partial sum up to the second-to-last term,
Subtracting this from the previous partial sum, we have
We're given that the sums must add to
But taking the differences now yields
and there is only one
Answer:
pepepopo
Step-by-step explanation:
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