A number theory problem by Paola Ramírez

Let be \(n\) a positive integer which satisfies the following conditions:

  • \(n\) is even.
  • \(n\) divided by 5 leaves a remainder of 1.
  • \(n\) is divisible by 7.
  • \(n<1000\).
  • The sum of digits of \(n\) is 23.

Find \(n\).

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