Question

If n^4+n^2+1 is a prime no. find the possible values of n
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Answer 1

Answer:

Step-by-step explanation:

Obviously, n has to be a prime number. So there is no need to test n=0 or n=1.

Then, with n=2, we see that n+2 can't prime because that's obviously divisible by 2. No need to look at n=4 either. In fact, we don't need to consider any other even n.

Moving on to n=3, we obtain the primes 3, 5, 7. Ding, ding, ding!

With n=5, we get the prime 7 but also 9=32.

And with n=7, we get n+4=11, but n+2=9=32.

Look at this problem modulo 6: if n is odd, it has to be 1 or 5(mod6) to not be a multiple of 3. But if n≡1(mod6), then n+2≡3(mod6), or if n≡5(mod6), then n+4≡3(mod6)

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Answer 2

Answer:

I hope it may help you

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