Given that n is an integer and the fourth power of n is - 16 & # 178; N + 100 is a prime number, find n
Original formula = n ^ 4 + 20n & # 178; + 100-36n & # 178;
=(n²+10+6n)(n²+10-6n)
One of the prime numbers is 1 and the other is prime
n²+10+6n=1
N = - 3, then n & # 178; + 10 + 6N = 1
It's not prime
n²+10-6n=1
Then n = 3, n & # 178; + 10 + 6N = 37
establish
So n = 3
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