Question

number of values of x belongs to N for which x^4+4 is prime​

Answer 1

Answer:

The question was tailored to be solved by Sophie Germain Identity, which is :

a4+4b4=(a2+2b2+2ab)(a2+2b2−2ab)

For the given question, put x=a and b=1 and factor the given expression as,

x4+4=(x2+2+2x)(x2+2−2x)

The case was as it is trivial for even values of x , but now clearly for all n>1 the given expression would yield only composite integers.

Therefore there are only two integers for which the given expression can yield prime numbers, −1 and +1