Primes

 

What prime is 4 greater than a perfect square and 9 less than the next perfect square?   

 

let P stand for the prime number

let x² stand for the first square

let (x+1)² stand for the next square   

 

x² + 4  =  P 

(x+1)² – 9  =  P  

 

therefore                          x² + 4  =  (x+1)² – 9  

 

                                        x² + 4  =  (x² + 2x + 1) – 9  

 

subtract x² from both sides     4  =  2x + 1 – 9  

 

combine like terms                12  =  2x

 

                                               x  =  6  

 

x² + 4  =  P  

36 + 4  =  40  

 

(x+1)² – 9  =  P 

49 – 9  =  40            P = 40 but 40 isn't prime so the problem has no answer 

_.