If $$n$$ is positive integer, find the value of n such that $$n^4-16n^2+100$$ is a prime number

Question

Uniteasy Admin · Accepted Answer

$$n^4-16n^2+100$$
$$=n^4+20n^2+100-36n^2$$
$$=(n^2+10)^2-(6n)^2$$
$$=(n^2+6n+10)(n^2-6n+10)$$ 
Since $$n^2+6n+10>1$$, to make the number prime $$n^2-6n+10$$ must be equal to 1, that is
$$n^2-6n+10 = 1$$
then
$$(n-3)^2 = 0$$
$$n=3$$
Checking
Substitute $$n=3$$ to $$n^2+6n+10$$
$$3^2+6	imes3+10 =37$$
Therefore
When $$n= 3, n^4-16n^2+100$$ is a prime numer

Question

Answer