Modular inverse
API · /modular-api
Modular Arithmetic API
healthy
4,017 Subscribers
Modular-arithmetic maths as an API, computed locally and deterministically with exact big-integer arithmetic. The power endpoint computes modular exponentiation, aᵇ mod m, by square-and-multiply, fast and exact even for the huge exponents used in cryptography. The inverse endpoint finds the modular multiplicative inverse a⁻¹ mod m with the extended Euclidean algorithm, returning the inverse when a and m are coprime and reporting the gcd when no inverse exists. The totient endpoint computes Euler's totient φ(n) — the count of integers from 1 to n coprime to n — with the prime factorization it comes from, and an optional Euler-theorem check that a^φ(n) ≡ 1 (mod n) for a coprime base. These are the building blocks of RSA and much of modern cryptography. Inputs are integers and can be passed as strings for very large values. Everything is computed locally and deterministically, so it is instant and private. Ideal for cryptography, security, blockchain and mathematics app developers, RSA and number-theory tools, and computer-science education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is modular arithmetic; for prime factorization and GCD use a number-theory API and for integer sequences a sequences API.
api.oanor.com/modular-api
API health
healthy- Uptime
- 100.00%
- Server probes · 24h
- Avg latency
- 85 ms
- Server probes · 24h
- Subscribers
- 4,017
- active
- Total calls
- 28
- last 7 days
Pricing
Pick a tier — billed monthly, cancel anytime.
Free
Free
- 3,000 calls / month
- 2 requests / second
- Hard cap (429 above quota, no overage)
- Modular add, multiply and inverse
- Exact big-integer arithmetic, no rounding
- Deterministic results, no upstream latency
Starter
€7.00 /month
- 25,000 calls / month
- 5 requests / second
- Hard cap (429 above quota, no overage)
- Modular exponentiation (pow) endpoint
- Euler totient and GCD/LCM helpers
- Arbitrary-precision big integers
- JSON responses with exact remainders
Pro
€19.00 /month
- 150,000 calls / month
- 15 requests / second
- Hard cap (429 above quota, no overage)
- Fast modexp for RSA-sized moduli
- Totient and CRT batch operations
- Higher rate limit for crypto workloads
- Priority compute path
Mega
€59.00 /month
- 1,000,000 calls / month
- 40 requests / second
- Hard cap (429 above quota, no overage)
- High-volume modular arithmetic at scale
- Bulk modexp and totient batches
- Top rate limit for production crypto pipelines
- SLA-grade deterministic compute
Built by
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Combinatorics API
Combinatorics maths as an API, computed locally and deterministically with exact arbitrary-precision integers. The factorial endpoint computes n! = 1·2·3···n (with 0! = 1) and returns it exactly as a string together with its digit count, so even very large factorials stay precise. The permutations endpoint counts ordered arrangements: without repetition nPr = n!/(n−r)! arrangements of r items chosen from n, and with repetition n^r, where each of the r positions may be any of the n items. The combinations endpoint counts unordered selections: without repetition the binomial coefficient nCr = n!/(r!·(n−r)!), and with repetition (multisets) C(n+r−1, r), where repeats are allowed. All results are computed with BigInt so they are exact no matter how large, returned as a string with the number of digits and a floating-point approximation when it fits. n and r are non-negative integers up to 100000. Everything is computed locally and deterministically, so it is instant and private. Ideal for probability, statistics, lottery, game-design, cryptography and education app developers, counting and odds tools, and discrete-maths teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is counting combinatorics; for modular arithmetic use a modular API and for descriptive statistics a statistics API.
api.oanor.com/combinatorics-api
Complex Number API
Complex-number maths as an API, computed locally and deterministically. The arithmetic endpoint adds, subtracts, multiplies or divides two complex numbers z₁ = a + bi and z₂ = c + di, returning the result in both rectangular (a + bi) and polar (modulus ∠ angle) form. The properties endpoint describes a single complex number — its modulus |z| = √(a² + b²), its argument in radians and degrees, its conjugate, its negation, its reciprocal and its polar form. The power endpoint applies De Moivre's theorem, zⁿ = rⁿ(cos nθ + i·sin nθ), to raise a complex number to any real power, and for a positive integer n it also returns all n distinct n-th roots, evenly spaced around the complex plane. The imaginary part defaults to zero, so real inputs work too. Everything is computed locally and deterministically, so it is instant and private. Ideal for engineering, signal-processing, electronics, physics and mathematics app developers, AC-circuit and phasor tools, and STEM education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is complex-number arithmetic; for plane-angle unit conversion use an angle API and for vectors a vector API.
api.oanor.com/complexnumber-api
Interpolation API
Interpolation maths as an API, computed locally and deterministically. The linear endpoint interpolates between two points, y = y0 + (y1 − y0)·(x − x0)/(x1 − x0), returning the value at a target x (or, given a target y, solving the x that produces it), the parameter t and whether the point lies outside the segment. The table endpoint does piecewise-linear interpolation within a table of (x, y) points supplied as comma-separated lists — it sorts the points, finds the two that bracket your query and interpolates between them, extending the nearest segment and flagging the result when you query outside the data range, ideal for calibration curves and lookup tables. The bilinear endpoint interpolates on a rectangular grid from four corner values, interpolating along x at each y-edge and then along y. Everything is computed locally and deterministically, so it is instant and private, and unlike regression it passes exactly through the supplied points. Ideal for engineering, data-visualisation, gaming, mapping and scientific-computing app developers, lookup-table and calibration tools, and numerical-methods education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is interpolation; for least-squares regression and correlation use a statistics API.
api.oanor.com/interpolation-api
Triangle Solver API
Triangle-solving maths as an API, computed locally and deterministically. The solve endpoint solves any triangle from three values — three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA/AAS), or the ambiguous two-sides-and-a-non-included-angle case (SSA) — using the law of cosines and the law of sines, and returns all three sides and angles, the perimeter, the Heron area and whether the triangle is acute, right or obtuse and equilateral, isosceles or scalene; for an ambiguous SSA input it also returns the second valid triangle. The right endpoint is a dedicated right-triangle solver from any two of the two legs, the hypotenuse and an acute angle, applying Pythagoras and basic trigonometry. The points endpoint builds a triangle from three cartesian vertices, giving the side lengths, the interior angles, the shoelace area and the centroid. Angles are in degrees. Everything is computed locally and deterministically, so it is instant and private. Ideal for education, CAD, surveying, game-development and engineering app developers, geometry and trigonometry tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This solves triangles; for areas and volumes of general shapes use a geometry API and for polygon point-set operations a polygon API.
api.oanor.com/triangle-api
Frequently asked questions
Quick answers about pricing, quotas, and integration.
How do I get an API key for Modular Arithmetic API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Modular Arithmetic API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Modular Arithmetic API?
Free tier allows 1 request per second. Paid plans scale up to 50 requests per second on the Mega tier. Hard limits return HTTP 429 above the quota — no surprise overage charges.
How much does Modular Arithmetic API cost?
Modular Arithmetic API has a free tier with 100 calls / month. Paid plans start at €7.00 / month with higher quotas and faster rate limits.
Can I cancel my subscription anytime?
Yes. Plans are billed monthly and you can cancel anytime from your billing dashboard. No long-term contracts and no cancellation fee.
Is Modular Arithmetic API GDPR-compliant?
All requests to Modular Arithmetic API go through our EU-based gateway. Your upstream API key never leaves our server and no personal data is shared with the upstream provider beyond the request you send.
Pick an endpoint from the list on the left to see its details and try it.
Code snippets
Sign up to get an API key, then call any path under your slug.
curl https://api.oanor.com/modular-api/SOME_PATH \
-H "x-oanor-key: oanor_test_..."const res = await fetch("https://api.oanor.com/modular-api/SOME_PATH", {
headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();$ch = curl_init("https://api.oanor.com/modular-api/SOME_PATH");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
$response = curl_exec($ch);import requests
r = requests.get(
"https://api.oanor.com/modular-api/SOME_PATH",
headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())Ratings
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