I reduced it to
$(2013-6)^{201} + (2013+6)^{201} - (2013-31)^{201} - (2013+31)^{201} $
But this way I only get option D. How do I check for the other options. (Multiple correct question)
2026-03-30 13:04:00.1774875840
$2007^{201} + 2019^{201} - 1982^{201} - 2044^{201}$ is divisible by which of the following?
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$2007^{201}+2019^{201}$ is divisible by $2007+2019=4026=2\cdot2013$ and
$1982^{201}+2044^{201}$ is divisible by $1982+2044=4026=2\cdot2013$.
Thus, our expression is divisible by $2013$.
The expression is an even number, $2019-1982=37$ and $2007-2044=-37$, which says that our expression is divisible by $74$.
Also, $2007-1982=-25$, $2019-2044=-25$, which says that our expression is divisible by $50$ and by $50\cdot37=1850.$