A PolyNoMials (corrected)

Algebra Level 3

f(x) is a 1000 degree polynomial (x-1)(x-2)...(x-1000)+x

if f(x) = x if 1 < x < 1000 1<x<1000 , when x is an integer

what is f(1001) (mod 10) ?


The answer is 1.

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2 solutions

Parveen Soni
Dec 5, 2014

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

Christian Daang
Dec 25, 2014

Solution:

Since f(x)=(x-1)(x-2)…(x-1000)+x,for f(x)=x if 1<x<1000 so,

f(1001)=(1000 999 998 1)+1001

=1000!+1001

But,we know that 1000!is divisible by 10 so,

(1000!+1001) Mod(10)≡0+1001 Mod(10)≡1 ∎

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