Do it without a calculator. I double-dare you

Number Theory Level 5

If the least solution for the equation

\[x^2 - 853777y^2 = 1\]

can be represented as \((x, y)\), where \(x\) and \(y\) are positive integers, find \(x + y\).

  • The least solution is the solution with the smallest values of \(x\) and \(y\)

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