The result of \(194^{595} \mod 1079\) is \(51\).

Do you need further details or have any questions? Here are 5 related problems:

1. What is \( 256^{300} \mod 1024 \)?
2. Solve \( 17^{125} \mod 539 \).
3. Can you calculate \( 9^{512} \mod 17 \)?
4. What is \( 245^{150} \mod 403 \)?
5. Compute \( 345^{198} \mod 789 \).

**Tip:** Modular exponentiation can be efficiently computed using the method of "exponentiation by squaring." This is especially useful for large powers.

Explore how to solve the modular exponentiation problem 194^595 mod 1079. This solution involves key concepts from number theory and modular arithmetic, using the method of exponentiation by squaring for efficient calculation. Ideal for high school and college students.

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