Description
Advance an integer residue by a supplied integer difference using numeric modulo arithmetic.
A sequence rule specifies how terms relate. Checking one transition, advancing a recurrence, and bounding an infinite tail answer different questions. A calculation from supplied coefficients assumes that rule; it does not infer it from observations.
Advance an integer residue by a supplied integer difference using numeric modulo arithmetic.
When to use this tool
Use it for arithmetic progression modular residue step when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter residue, difference, modulus. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read nextResidue. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Normalize the supplied difference modulo the positive integer modulus, add it to an in-range residue, and normalize again to obtain nextResidue.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| residue | Residue | Required. Safe integer; minimum 0. |
| difference | Signed safe-integer step; normalized modulo the positive modulus before addition. | Required. Safe integer. |
| modulus | Modulus | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| nextResidue | Next Residue | Required. Safe integer. |
{
"input": {
"residue": 8,
"difference": 5,
"modulus": 10
},
"output": {
"nextResidue": 3
}
}Limitations and assumptions
- All three inputs must be safe integers, with a positive modulus and residue below it. Intermediate addition still uses binary floating point and can lose integer precision near the safe-number limit; use exact decimal-integer arithmetic when that matters.
- The field tables describe structural bounds; the mechanics also state cross-field requirements. Malformed input shapes, disallowed keys, and invalid domains cause input errors. Results must remain finite and within the declared output contract. A successful false flag or zero placeholder is distinct from an error.
- Numeric arithmetic uses binary floating point. Exact comparisons have no hidden tolerance or decimal rounding; negative zero is exported as zero. Decimal-text integer operations retain the exactness specifically stated above.
Alternative or Complementary methods
For arithmetic progression modular residue step, check the source records and the supplied rule before comparing the result with another method. Use exact integer or symbolic arithmetic when a numerical equality is insufficient.
References
Similar or alternative tools
- Arithmetic Progression Modulus Residue
Calculate an exact arithmetic-progression term modulo a positive integer using decimal text.
- Arithmetic Progression One Term Deletion Gap
Calculate the gap between surviving arithmetic-progression neighbors after one missing term.