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Version
4.1
Size
2.07 Mb
Updated
1 month ago
Released
17 Aug 2013
Screenshots
Description
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.
Estimates
Availability
Devices
iPhone4
iPad2Wifi
iPad23G
iPhone4S
iPadThirdGen
iPadThirdGen4G
iPhone5
iPodTouchFifthGen
iPadFourthGen
iPadFourthGen4G
iPadMini
iPadMini4G
iPhone5c
iPhone5s
iPadAir
iPadAirCellular
iPadMiniRetina
iPadMiniRetinaCellular
iPhone6
iPhone6Plus
iPadAir2
iPadAir2Cellular
iPadMini3
iPadMini3Cellular
iPodTouchSixthGen
iPhone6s
iPhone6sPlus
iPadMini4
iPadMini4Cellular
iPadPro
iPadProCellular
iPadPro97
iPadPro97Cellular
iPhoneSE
iPhone7
iPhone7Plus
iPad611
iPad612
iPad71
iPad72
iPad73
iPad74
iPhone8
iPhone8Plus
iPhoneX
iPad75
iPad76
iPhoneXS
iPhoneXSMax
iPhoneXR
iPad812
iPad834
iPad856
iPad878
iPadMini5
iPadMini5Cellular
iPadAir3
iPadAir3Cellular
iPodTouchSeventhGen
iPhone11
iPhone11Pro
iPadSeventhGen
iPadSeventhGenCellular
iPhone11ProMax
iPhoneSESecondGen
iPadProSecondGen
iPadProSecondGenCellular
iPadProFourthGen
iPadProFourthGenCellular
iPhone12Mini
iPhone12
iPhone12Pro
iPhone12ProMax
iPadAir4
iPadAir4Cellular
iPadEighthGen
iPadEighthGenCellular
iPadProThirdGen
iPadProThirdGenCellular
iPadProFifthGen
iPadProFifthGenCellular
iPhone13Pro
iPhone13ProMax
iPhone13Mini
iPhone13
iPadMiniSixthGen
iPadMiniSixthGenCellular
iPadNinthGen
iPadNinthGenCellular
iPhoneSEThirdGen
iPadAirFifthGen
iPadAirFifthGenCellular
iPhone14
iPhone14Plus
iPhone14Pro
iPhone14ProMax
iPadTenthGen
iPadTenthGenCellular
iPadPro11FourthGen
iPadPro11FourthGenCellular
iPadProSixthGen
iPadProSixthGenCellular
Pricing by country
| Country | Price |
|---|---|
| Canada | 2.99 CAD |
| China | 15 CNY |
| France | 1.99 EUR |
| Germany | 1.99 EUR |
| Italy | 1.99 EUR |
| Netherlands | 1.99 EUR |
| Portugal | 1.99 EUR |
| Spain | 1.99 EUR |
| Poland | 1.09 EUR |
| UK | 1.99 GBP |
| India | 199 INR |
| Japan | 300 JPY |
| Korea, Republic Of | 3300 KRW |
| Poland | 9.99 PLN |
| Russia | 199 RUB |
| Turkey | 99.99 TRY |
| USA | 1.99 USD |
| Korea, Republic Of | 2.19 USD |
| Ukraine | 1.99 USD |
