Question

how many primes are there in the form\[m^4+4n^4\]

Answer 1

Let p =m^4 + 4n^4
THEN
p=(m^2+2n^2-2mn)(m^2+2n^2+2mn)

Answer 2

where P is a prime number....... NOW,
((m^2+2n^2-2mn)=1
AND (m^2+2n^2+2mn)=p

Answer 3

Am i doing correct?

Answer 4

yup

Answer 5

and then?

Answer 6

So, we need to solve that two equations

Answer 7

Further simplification will get
1+4mn=p

Answer 8

So, m=1 and n=1 is one of the solution

Answer 9

emm...dont look for p

prime number cant be has 2 factors so just look for m,n from m^2+2n^2-2mn=1

Answer 10

m^2+2n^2-2mn=1
(m^2-2mn+n^2)+n^2=1
(m-n)^2=1-n^2
m=n+- (1-n^2)^1/2

Answer 11

So, n cannot be greater than 1

Answer 12

Thus, the only solution is when n=1

Answer 13

n=m=1 and p=5

well done saura

Answer 14

Thanx

Answer 15

note that when one of m or n is greater than 1 then

m^2+2n^2-2mn>1

Answer 16

so both of them must be 1

Answer 17

Oh ya.... that way can also be done