The prime numbers a, b and c are such that a+b^2 =4 c^2 . Determine the sum of all possible values of a+b+c .

Step-by-step solution

aligned & 4 c^2-b^2=a & (2 c-b)(2 c+b)=a & 2 c-b=1 and 2 c+b= a & 4 c=a+1 and 2 b=a-1 aligned If c 5 than c must be of the type 6 1 for N Let c=6 1 , then a=24 +3 or 24 -5 24 +3 is not a prime, so c=6 -1 and a=24 -5 then b= 24 -6 2 =12 -3 , which is not a prime. So c cannot be greater than 5 . If c=3 then a=7 and b=5 and If c=2 then a=7 and b=3 Sum of possible values of a+b+c=31