11do u mean,
If n4+4n is prime, then number of values of n,nEN is...???
5 Answers
11
1Lemma : -
If " n " is odd , then " 2 n - 2 " can be written down as " 4 k " , where " k " ( ≥ 0 ) E { I } .
Proof : -
If " n " is odd , then " n - 1 " must be even , i.e , " n - 1 " is of the form " 2 k " .
Hence , " 2 ( n - 1 ) " or " 2 n - 2 " is of the form " 4 k " .
11@ricky,
how does this help here.. :(
in this problem, i can see only that n can not take even values..
and n=1 gives a prime number...
1Sorry , I now finish my proof .
If " n " be odd , then let " 2 n - 2 = 4 k " .
Now ,
n 4 + 4 n = n 4 + 4 . 2 2 n - 2 = ( n 2 + 2 . n . 2 k + 2 2 k ) ( n 2 - 2 . n . 2 k + 2 2 k )
Since we can factorise the given expression , therefore it cannot be a prime .
We didn't consider the case " n = 1 " , for which value only the expression generates a prime number , " 5 " .