Integer mod pow

integer-mod-pow · version 1.0.0 · Numbers & math · free, no key needed

Compute base^exponent mod modulus exactly using fast modular exponentiation.

Use when you need to: integer mod pow · modular exponentiation · modular power.

Supported

• integer mod pow
• modular exponentiation
• modular power
• fast exponentiation mod m

Not supported

• negative exponent
• modular inverse
• floating-point power

Behavior

• base and exponent are canonical integer strings; modulus is a canonical integer string.
• exponent must be non-negative; a negative exponent is rejected (use integer-mod-inverse first for negative exponents).
• modulus must be a positive canonical integer; zero and negative moduli are rejected.
• base may be negative or exceed the modulus; it is reduced modulo modulus before exponentiation, matching mathematical convention (result is always in [0, modulus)).
• modulus 1 always yields 0.
• The result is base^exponent mod modulus as a canonical non-negative integer string, computed by binary exponentiation so exponent size does not cause a slow loop.
• Each input may have at most 1000 digits excluding sign; the result has fewer digits than modulus.

Input

• base (string, required): min length 1; max length 1001
• exponent (string, required): max length 1000; pattern ^(0|[1-9][0-9]*)$
• modulus (string, required): min length 1; max length 1001

Output

• value (string, required)

Limits

• max digits: 1000

Example

Request input:

{
  "base": "4",
  "exponent": "13",
  "modulus": "497"
}

Response:

{
  "result": {
    "value": "445"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "integer-mod-pow",
  "version": "1.0.0",
  "input": {
    "base": "4",
    "exponent": "13",
    "modulus": "497"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-mod-pow/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"base":"4","exponent":"13","modulus":"497"}'

The machine-readable contract is at /v1/tools/integer-mod-pow/versions/1.0.0.

CLI

node cli.mjs run integer-mod-pow 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Integer mod inverse: Compute the modular multiplicative inverse of a modulo modulus, when it exists.
• Rational power: Raise a rational number to an integer exponent and return the exact reduced result.
• Integer CRT: Solve a system of integer congruences (x ≡ remainder mod modulus) with the Chinese Remainder Theorem.
• Array integer adjacent diff: Replace an array of canonical integer strings with consecutive first differences.
• Array integer clamp: Clamp an array of canonical integer strings to optional inclusive min and max bounds.
• Array integer cumulative sum: Replace an array of canonical integer strings with equal-length prefix sums.