Free · Modular arithmetic
Integer Power Remainder
Calculate an integer power remainder across the full captured input range without constructing the enormous power.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
3^5 mod7 =5.
base^exponent mod modulus
Worked example
Enter these known values and leave the other values blank.
- x (base)
- 3
- y (exponent)
- 5
- n (divisor)
- 7
- Power modulo
- 5
Assumptions and limitations
- Base, exponent and modulus are positive integers no greater than 9e15.
- The result is the least nonnegative remainder. A modulus of 1 returns 0; the output is forward-only.
Common questions
Can I enter a negative value?
This captured model requires positive inputs.
What is the output range?
The selected residue lies from zero through one less than the modulus.
References
Calculate remainders with exact integer arithmetic for positive integer inputs up to 9,000,000,000,000,000. Keep all inputs, the forward-only result and complete equation explanations.