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