Prove that 4 is the only perfect square that is one more than a prime number
+15 I would say the answer is, No. I would say that because if you check the next perfect square, 8, it is one above 7 which is a prime number. (correct me if I'm wrong)
+15 I am very sorry. I am a bit rusty on my elementary math... it has been about a year since I've had a refresher for it. Let me fix that mistake and take a bit of time into that. I would say it is the only perfect square that is one above a prime number I went all the way to 263.
+118608 A perfect square is of the form x^2 where x is a positive whole number
One less than a perfect square is x^2 -1
\(x^2-1=(x-1)(x+1)\)
If this is a prime number then the smaller factor must be 1
x-1=1
x=2
x^2-1 = 3
Hence 3 is the only prime number that is followed by a perfect square.
+118608 I shall try 
A perfect square is of the form x^2 where x is a positive whole number
One less than a perfect square is x^2 -1
\(x^2 -1\) is the difference of 2 squares.
difference means subtract and the two squares are x^2 and 1^2
You need to memorize this factorization.
\(\boxed{a^2-b^2=(a-b)(a+b)}\)
so \(x^2-1^2=(x-1)(x+1)\)
If this is a prime number then the smaller factor must be 1
the factors are (x-1) and (x+1)
since x is a positive whole number, the smallest one will be x-1
therefore x-1 must equal 1
so x must equal 2
