How to calculate big exponents (with modular division involved)?

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I found the following equation online when working with cryptography.

1702^2732 x 2083^2526 = 704 mod 3119

Now I'd like to understand the math behind:

  • how do we calculate exponentiation with number that high?
  • how did we get this mod part?

From the article, it looks like the calculation has been done by hand, with no computer involved.