Square the Factorial

Number Theory Level 5

If \[x^{2} - z! = y^{2}\]

  • \(x,y \in I \)

  • \(z\) is \(10's\) place digit of \(x\) and \(z \ne 0\) i.e If \(x=23\) then \(z=2\)

Then let \(S_{x}\) be the sum of the smallest 4 Positive values of \(x\) that satisfy the above equation

The sum of the corresponding positive values of \(y\) be \(S_{y}\).

Then find the value of \(S_{x} + S_{y}\).

NOTE :- Corresponding value of \(y\) is the value that you get by putting the value of \(x\) in the equation.

  • \(x\) can't be a single digit number but it can contain two or more digits.

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