That's a lot of digits

Number Theory Level 3

\[J = \overline {{ababababab....ab}}_n\]

The number of \(ab\) pairs in \(J\) is even. \(a\) and \(b\) are \(< n\)

True or false:

\(\quad \) \(J\) is divisible by \(n^2+1\).

Clarification: The subscript means number base \(n\). The line above the number means that \(a, b\) are digits of the number. \(a, b < n\).

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