Description
Calculate an exact arithmetic-progression term modulo a positive integer using decimal text.
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.
Calculate an exact arithmetic-progression term modulo a positive integer using decimal text.
When to use this tool
Use it for arithmetic progression modulus residue when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter first, step, index, modulus. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read residue. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Evaluate first + index*step with exact decimal-integer parsing and reduce it modulo a positive integer modulus. Normalize the residue into zero through modulus minus one and return decimal text.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Text; maximum UTF-16 length 8192. |
| step | Step | Required. Text; maximum UTF-16 length 8192. |
| index | Zero-based selected index, unless a different convention is stated in the mechanics. | Required. Safe integer; minimum 0. |
| modulus | Modulus | Required. Text; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residue | Residue | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"first": "3",
"step": "4",
"index": 5,
"modulus": "7"
},
"output": {
"residue": "2"
}
}Limitations and assumptions
- Index is a nonnegative safe integer and text integer lengths are bounded. This computes a zero-based progression term's residue, not a cryptographic operation or a fitted modular recurrence.
- 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.
Alternative or Complementary methods
For arithmetic progression modulus residue, 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 Modular Residue Step
Advance a numeric residue by a supplied difference under floating-point modulo arithmetic.
- Arithmetic Progression One Term Deletion Gap
Calculate the gap between surviving arithmetic-progression neighbors after one missing term.