f(x) is a 1000 degree polynomial (x-1)(x-2)...(x-1000)+x
if f(x) = x if , when x is an integer
what is f(1001) (mod 10) ?
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f(1001)=1000!+1001=unit digit as 1(even last four digit as 1001 as 1000! has no. of trailing zeros) so when any number with unit digit as 1 divided by 10 gives remainder as1