Description
For positive integer exponent return negative=(base<0 and exponent odd) and evenPower=(exponent even).
Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.
For positive integer exponent return negative=(base<0 and exponent odd) and evenPower=(exponent even).
When to use this tool
Use Integer Perfect Power Parity Witness when you need this exact stated integer sign, bound, division, comparison, or factor component.
How to use the tool and how it works
- Enter base, exponent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read negative, evenPower. Inspect negative, evenPower before interpreting the associated values.
For positive integer exponent return negative=(base<0 and exponent odd) and evenPower=(exponent even).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| base | Base | Required. Safe integer. |
| exponent | Exponent | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| negative | Negative | Required. Boolean. |
| evenPower | Even Power | Required. Boolean. |
{
"input": {
"base": -3,
"exponent": 4
},
"output": {
"negative": false,
"evenPower": true
}
}Limitations and assumptions
- The integer power is not evaluated. A zero base produces negative=false, and these sign/parity flags do not establish that an unrelated number is a perfect power.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.
References
Similar or alternative tools
- Reciprocal Integer Fraction Order Witness
For nonzero integer first and second return originalOrder=sign(first-second) and reciprocalOrder=sign((second-first)/(first*second)).
- Integer Negabinary Digit Parity
Count the ones and digit length in the canonical base −2 expansion, including one zero digit for zero.