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What is the remainder of 17762011!\displaystyle {1776}^{2011!}17762011! upon division by 2000?2000?2000?
What is the remainder of 22!{22}!22! upon division by 23?23?23?
What is the remainder of 14410\displaystyle {144}^{10}14410 upon division by 13?13?13?
What is the remainder of mmm satisfying 11+12+13+⋯+133=m33!\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{33}=\frac{m}{33!}11+21+31+⋯+331=33!m upon division by 17?17 ?17?
For three integers x,x,x, yyy and z,z,z, which of the following can NOT be expressed as x2+y2+5z2?x^2+y^2+5z^2 ?x2+y2+5z2?
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