Download your Word document
Fermat's Little Theorem Check result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Fermat's Little Theorem Check — result sheet
Check the modular result described by Fermat's little theorem for a prime modulus.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For prime p and p not dividing a, a^(p - 1) = 1 (mod p).
The calculator first verifies that p is prime, then evaluates a^(p-1) modulo p and identifies the separate case where p divides a.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Base a — minimum -1000000000; maximum 1000000000
- Prime p — minimum 2; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Base a | 3 |
| Prime p | 7 |
3^6 modulo 7 is 1, so the theorem condition holds.
Assumptions and limits
- The modulus p must be prime.
- The theorem's conclusion of 1 applies only when p does not divide a.
- This checks the congruence numerically and is not a primality proof for arbitrary large inputs.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.