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Let \(n\) be an integer such that: \(n^2 = 17p + 1\), where \(p\) is a prime number.
  1. Write \(17p\) as a product of factors in terms of \(n\).
  2. Show that \(n\) is of the form \(n = 17k + 1\) or \(n = 17k - 1\) with \(k \in \mathbb{Z}\). State the theorem used.
  3. Show that only one value of \(k\) is suitable for \(n\) and \(p\) to exist according to the conditions. Deduce the values of \(n\) and \(p\).

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