![(POL 3)](/media/m/3/b/2/3b29653c5b6e5bfe33fb334f8ad0027a.png)
Given a polynomial
![f(x)](/media/m/3/f/4/3f40d68090aa4fb60a440be4675c7aca.png)
with integer coefficients whose value is divisible by
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
for three integers
![k, k + 1,](/media/m/e/5/a/e5aa040dc047458a7226c8742cfd30f0.png)
and
![k + 2](/media/m/4/b/6/4b652ef42328d9fad48c74622e0d39cc.png)
. Prove that
![f(m)](/media/m/0/f/f/0ff83359cffe1db2b53c99d5197fd294.png)
is divisible by
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
for all integers
%V0
$(POL 3)$ Given a polynomial $f(x)$ with integer coefficients whose value is divisible by $3$ for three integers $k, k + 1,$ and $k + 2$. Prove that $f(m)$ is divisible by $3$ for all integers $m.$