# Modular Arithmetic — Calculate in remainders mod n

> Calculator for arithmetic modulo N with support for large numbers and advanced operations. (iPhone/iPad app by Benjamin Burton.)

- Source: https://appshunter.io/ios/app/modular-arithmetic/id687735575 (this page in markdown: same URL + `.md`)
- Developer: [Benjamin Burton](https://appshunter.io/developer/687735578)
- Category: Education, Utilities
- Price: $1.99
- Rating: 5.00/5 from 4 App Store ratings · 2 written reviews indexed
- Age rating: 4+
- Requires: iOS 12.0 · 2 MB
- Languages: American English
- Released: 2013-08-17
- Data updated: 2026-08-12
- Monetization: paid
- User reviews in markdown: https://appshunter.io/ios/app/modular-arithmetic/id687735575/reviews.md

## What is Modular Arithmetic?

A calculator for arithmetic modulo N.  It lets you choose a fixed modulus, and then make lots of calculations without having to press a "mod" button again and again.  It also:

- follows the order convention;
- supports arbitrarily large numbers;
- performs fast modular division and exponentiation;
- can show a full transcript of your calculation.

Modular arithmetic is a "calculus of remainders".  It features throughout mathematics and computer science, and has applications from cryptography to barcodes to music.

The basic idea is that you choose a modulus N, and then reduce every number to one of the integers 0,1,2,...,N−1 according to what remainder it leaves when dividing by N.

For example, using a modulus of 17:

40 ≡ 6 (since 40 ÷ 17 leaves a remainder of 6);
17 ≡ 0 (since 17 ÷ 17 leaves no remainder at all).

Arithmetic follows these same rules.  Still using a modulus of 17:

15 + 7 ≡ 5 (since 22 ≡ 5);
3 × 9 ≡ 10 (since 27 ≡ 10);
5 ^ 3 ≡ 6 (since 125 ≡ 6).

Subtraction and division behave in a way that complements addition and multiplication:

−1 ≡ 16 (since 16 + 1 = 17 ≡ 0);
1/2 ≡ 9 (since 9 × 2 = 18 ≡ 1);
4 - 7 ≡ 14 (since 14 + 7 = 21 ≡ 4);
7 ÷ 3 = 8 (since 8 × 3 = 24 ≡ 7).

There are no negative numbers or fractions: like −1 and 7 ÷ 3 in the examples above, these are also reduced to one of 0,1,...,N−1.

As usual, you cannot divide by zero.  You also cannot divide if the right hand side has any common factors with the modulus.  If we change our modulus to 10, then the following operations all generate errors:

3 ÷ 20 (since 20 ≡ 0);
7 ÷ 8 (since 8 and 10 have a common factor of 2).

Integers can be arbitrarily large.  For instance, if we set our modulus to 2305843009213693951 (a Mersenne prime), then:

5 ^ 2305843009213693950 ≡ 1 (by Fermat's little theorem).

The code is written carefully, and is backed up by a thorough suite of 186 automated tests.

This app supports external keyboards, Siri Shortcuts, and (on iPad) Slide Over, Split View, and multiple windows.

## Key features

- Fixed modulus selection
- Arbitrarily large numbers
- Fast modular division and exponentiation
- Full calculation transcript
- Order of operations convention
- External keyboard and Siri Shortcuts support

## Recent user reviews (2 of 2)

All indexed reviews: https://appshunter.io/ios/app/modular-arithmetic/id687735575/reviews.md

### 5/5 — super fast & helpful unique app

*2014-02-04*

helped me with my studies tremendously

### 5/5 — Finally

*2014-01-16*

Finally a simple modular calculator app, thank you, useful for working through problems in number theory books.

## Frequently asked questions about Modular Arithmetic

### What is Modular Arithmetic?

Modular Arithmetic is a system of arithmetic for integers where numbers 'wrap around' upon reaching a certain value—the modulus. It's like a clock, where after 12, you go back to 1. This app allows you to perform calculations within this system.

### What are the key features of Modular Arithmetic?

Modular Arithmetic allows you to set a fixed modulus for repeated calculations, supports arbitrarily large numbers, performs fast modular division and exponentiation, and can display a full transcript of your calculations. It also follows the standard order of operations.

### What devices does Modular Arithmetic support?

Modular Arithmetic is available on Mac, iPhone, iPad, and iPod. It also offers features like Slide Over, Split View, and multiple windows on iPad, along with external keyboard and Siri Shortcuts support.

### How does Modular Arithmetic handle division?

The app performs fast modular division. However, division by zero is not allowed, and you cannot divide if the divisor shares any common factors with the modulus. For example, with a modulus of 10, you cannot divide by 20 or 8.

### Is Modular Arithmetic suitable for advanced users?

Yes, the app supports arbitrarily large numbers and advanced operations like modular exponentiation, making it suitable for complex mathematical and computer science applications, including cryptography. It is backed by 186 automated tests for reliability.

### What is the price of Modular Arithmetic?

Modular Arithmetic is a paid application, priced at $1.99. There are no in-app purchases or advertisements, offering a straightforward purchase experience.

### How often is Modular Arithmetic updated?

The app was last updated on September 23, 2024, indicating active development and maintenance. Its latest version is 4.1.

### What is the age rating for Modular Arithmetic?

Modular Arithmetic has an age rating of 4+, making it accessible for a wide range of users interested in learning mathematical concepts.

## Version history (last 5 releases)

### 4.1 — 2024-09-23

Added dark and tinted icons for iOS 18.

### 4.0 — 2020-11-30

- Supports multiple windows on iPad, so you can run two calculators side by side.
- Updated to run nicely on macOS.
- Other minor updates for iOS 14.

### 3.5 — 2019-09-25

Now supports dark mode in iOS 13.

### 3.4 — 2019-02-07

Added support for Siri Shortcuts.

### 3.3 — 2018-11-27

Supports external keyboards.
The iPad version now supports Slide Over and Split View.
Reordered digits to match a keyboard number pad (7-9 at the top).
Updated for the new 11-inch and 12.9-inch iPad Pro (late 2018).

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## More apps by Benjamin Burton

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All apps by Benjamin Burton: https://appshunter.io/developer/687735578

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*Data collected daily from the US App Store and indexed by [AppsHunter](https://appshunter.io/). User reviews are verbatim App Store reviews. Ratings, prices and chart positions refresh continuously; this snapshot is from 2026-08-12.*