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number of values of x belongs to N for which x 4 +4 is prime. plz help me out

number of values of x belongs to N for which x4 +4 is prime. plz help me out
 

Grade:12

3 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
If x is even then obviously the number is not prime
Hence the unit place of x should be 1,3,5,7,9
and for unit place
1,3,7,9
x4has unit place = 1 and hence x4+4 will have unit place =5 which will be always not prime except when x=1

Now for x with unit digit 5 it will never be prime
Hence x=1 is the only answer
Ankit Jaiswal
165 Points
8 years ago
Thanks sir,
But i did not get why for units place as 5 x4 +4 will not be prime??
What i think is that when we pu the units place as 5 we will get the ans with the unit 9 which can be prime
 
 
mycroft holmes
272 Points
7 years ago
x4+4 = (x2+2x+2)(x2-2x+2)
 
The first factor is at least 3 when x is natural. The second factor equals 1 only when x=1. Checking back we see that when x=1, the expression equals 5 which is prime.
 
Hence x=1 is the unique value of x for which x4+4 is prime with x a natural number
 
 

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