1. What is Power Mod?

Power Mod (modular exponentiation) calculates the remainder when a number raised to a power is divided by a modulus. It's expressed as \( a^b \mod m \) and is fundamental in number theory and cryptography.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( a \) — Base number
• \( b \) — Exponent
• \( m \) — Modulus

Explanation: The calculation is performed efficiently using the property that \( (a \times b) \mod m = [(a \mod m) \times (b \mod m)] \mod m \).

3. Applications of Power Mod

Details: Modular exponentiation is crucial in public-key cryptography (RSA algorithm), primality testing, hash functions, and computer algebra systems.

4. Using the Calculator

Tips: Enter positive integers for all values. The modulus must be greater than 0. For large exponents, the calculation may take longer.

5. Frequently Asked Questions (FAQ)

Q1: Why is power mod important in cryptography?
A: It allows efficient computation of very large exponentiations modulo a number, which is fundamental to many encryption algorithms.

Q2: What's the difference between power and power mod?
A: Power calculates \( a^b \) directly, while power mod calculates the remainder when \( a^b \) is divided by m.

Q3: Can this handle negative numbers?
A: This calculator is designed for non-negative integers only. For negative numbers, additional modulo arithmetic rules apply.

Q4: Is there a more efficient algorithm for large exponents?
A: Yes, the "exponentiation by squaring" method is more efficient for very large exponents.

Q5: What happens if modulus is 1?
A: Any number modulo 1 is 0, since division by 1 always leaves a remainder of 0.