Perfect Digital Invariant Checker

Perfect digital invariant with independent fixed power(not automatically decimaldigitlengthasArmstrong), exactBigIntdigitpowers≤128. Explicit bounded resource/branch and actual observations or independently verified parameters; no unproved infinite assertion certified.

Description

A perfect digital invariant equals the sum of its decimal digits raised to a specified fixed power.

A perfect digital invariant equals the sum of its decimal digits raised to a specified fixed power.^[1]

This tool checks that exact integer relation without choosing the power from digit length automatically.

When to use Perfect Digital Invariant Checker

This tool checks that exact integer relation without choosing the power from digit length automatically.

How to use Perfect Digital Invariant Checker and how it works

Prepare canonical decimal, independently specified digit power, using the input definitions and matching units below.
Enter the required fields and run Perfect Digital Invariant Checker.
Read result.exactDigitPowerSum, result.isSpecifiedPowerInvariant using the units, signs and ordering explained below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
actualCanonicalDecimal	Canonical nonnegative integer string, at most 128 digits, without signs or leading zeros except zero itself.	string	Required; other constraints below
actualIndependentlySpecifiedDigitPower	Actual Independently Specified Digit Power. Use the units and matching context stated in the calculation below.	number	Required; finite; other constraints below

Require canonical nonnegative decimal input up to 128 digits and specified digit power integer 1–128. Sum exact BigInt digit powers and return the decimal sum and whether it equals the input integer. Zero raised to a positive power contributes zero. The power is independently supplied rather than inferred from digit length.

digitPowerSum=sum(digit^specifiedPower); invariant=(digitPowerSum==input)

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.exactDigitPowerSum	Exact decimal-string sum of digit powers under the supplied fixed exponent.	string
result.isSpecifiedPowerInvariant	Whether the exact supplied-power digit sum equals the input integer.	boolean

json

{
  "input": {
    "actualCanonicalDecimal": "153",
    "actualIndependentlySpecifiedDigitPower": 3
  },
  "output": {
    "result": {
      "exactDigitPowerSum": "153",
      "isSpecifiedPowerInvariant": true
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Untouchable Number Checker for a complementary operation: An untouchable integer is absent from the range of the sum-of-proper-divisors function under a specified domain convention.

Use Superfactorion Checker for a complementary operation: A superfactorion uses the sum of superfactorials of its decimal digits, with the empty product at zero equal to one.

References

Perfect Digital Invariant Checker — tool.io

Similar or alternative tools

Untouchable Number Checker
An untouchable integer is absent from the range of the sum-of-proper-divisors function under a specified domain convention.
Superfactorion Checker
A superfactorion uses the sum of superfactorials of its decimal digits, with the empty product at zero equal to one.