n = x2 + 1
n = y3 - 1
x2 + 1 = y3 - 1
x2 = y3 - 2
x = (y3 - 2).5
This means that you need to find all cubes where subtracting 2 yields a square:
Cubes:
1, 8, 27, 64, 125,...
(-2):
-1, 6, 25, 62, 123,...
(27,25) works.
n = 26
64
It is 64 which is also a square number
123 is two less than 53 = 125 and two more than 112 = 121
26
It is: 81
26
123
3cubed is 27, 5 squared is 25. Answer is 26
64
eight ( 8 )
87 is the only 2-digit number that is 6 greater and 13 less than a square, but it is not prime.
It is 64 which is also a square number
0, 1 and 64
123 is two less than 53 = 125 and two more than 112 = 121
For a number to be both a square and a cube, it would have to be a sixth power. There are three sixth powers less than 100: 0^6 = 0, 1^6 = 1 and 2^6 = 64.
6859. Cube root of 9999 is 21.54, so find the largest prime number less than that (19), then cube that number. 19^3=6,859
2 digit number which is square number less than 42 but greater than 29 = 36square numbers are 2, 9, 16, 25, 36, 49,...