1994 AIME Problems/Problem 3

Problem

The function $f_{}^{}$ has the property that, for each real number $x,\,$

$f(x)+f(x-1) = x^2\,$

.

If $f(19)=94,\,$ what is the remainder when $f(94)\,$ is divided by 1000?

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1994 AIME (Problems • Answer Key • Resources)
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