BetterExplained
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Fun With Modular Arithmetic – BetterExplained
Divide by 3 and take the remainder (aka mod 3). You’ll have groups “0”, “1” and “2”. In programming, taking the modulo is how you can fit items into a hash table: if your table has N entries, convert the item key to a number, do mod N, and put the item in that bucket (perhaps ...
system of algebraic operations defined for remainders under division by a fixed positive integer; system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus
Wikipedia
en.wikipedia.org › wiki › Modular_arithmetic
Modular arithmetic - Wikipedia
2 weeks ago - This is because the hour hand makes ... we write 15 ≡ 3 (mod 12), so 7 + 8 ≡ 3 (mod 12). Similarly, if one waits 8 hours and then 8 more hours (thus 16 hours in total), the clock will show the same time change as if one waited 4 hours....
me, a 3 mod 4 prime, when the 1 mod 4 primes catch up to us: 😡😡🤬🤬🤬
Unintelligible, but cute More on reddit.com
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October 29, 2024Basic Question: 1 mod 4
That they end up in a smaller number in three steps does not exclude the possibility of them getting bigger in the steps after that. You aren't guaranteed that after dividing by four you will get a number that is 1 mod 4. More on reddit.com
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January 31, 2024when we talk about mod and reminder, what exactly are the reminders here, for example 3mod4 and -1mod4 how come the reminder is 3?
For integers a and b, the remainder of division of a by b is the smallest non-negative integer r for which there exists an integer q such that a = qb + r. More on reddit.com
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June 10, 2023How come -7 mod 3 is 2?
Here’s a way to think about it that could help. In “mod 3”, each integer has to be in (exactly) one of three equivalency classes: 0, 1, or 2. You can list elements in each, keeping in mind that consecutive elements in each class are distanced from each other by the modulus (in this case, 3). The “0 class” contains { …, -9, -6, -3, 0, 3, 6, 9, … }. All elements in this set are equivalent to 0 mod 3. Each element can be achieved by starting at 0 and going up or down, counting by 3. The “1 class” contains { …, -8, -5, -2, 1, 4, 7, 10, … }. All elements in this set are equivalent to 1 mod 3. Each element can be achieved by starting at 1 and going up or down, counting by 3. The “2 class” contains { …, -7, -4, -1, 2, 5, 8, 11, … }. All elements in this set are equivalent to 2 mod 3. Each element can be achieved by starting at 2 and going up or down, counting by 3. More on reddit.com
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June 19, 2024How much is 17 mod 3?
17 mod 3 equals 2 since dividing 17 by 3 gives a quotient of 5 and a remainder of 2. The remainder is the result of the modulus operation. In simpler terms, 17 mod 3 = 2.
omnicalculator.com
omnicalculator.com › math › modulo
Modulo Calculator
How to calculate modulo division?
To calculate modulo division: subtract the divisor from the dividend until the resultant is less than the divisor.
omnicalculator.com
omnicalculator.com › math › modulo
Modulo Calculator
What are the components of modulo division?
The components of modulo division are dividend, divisor, quotient, and remainder. The remainder is the answer or end result of the operation.
omnicalculator.com
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Modulo Calculator
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Omni Calculator
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Modulo Calculator
May 8, 2025 - That's exactly the case when you can use modulo! 10 mod 3 = 1.
Reddit
reddit.com › r/okbuddyphd › me, a 3 mod 4 prime, when the 1 mod 4 primes catch up to us: 😡😡🤬🤬🤬
r/okbuddyphd on Reddit: me, a 3 mod 4 prime, when the 1 mod 4 primes catch up to us: 😡😡🤬🤬🤬
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ModDB
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Mods for Games - ModDB
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Calculators.org
calculators.org › math › modulo.php
Modulo Calculator
Britannica notes that in modular ... and the mod is subtracted from the sum as many times as possible. This diminishes the sum to a number M, which is between 0 and N – 1. In his book, Gauss included a notation with the symbol ≡, which is read as “is congruent to.” Instead of the usual = symbol, the three horizontal line segments both signify equality and definition. For instance, if we add the sum of 2, 4, 3 and 7, the ...
Visual Fractions
visualfractions.com › calculator › modulo › what-is-3-mod-4
What is 3 mod 4? (3 modulus 4)
Learn how to find out what 3 mod 4 is in this simple, step-by-step guide.
Published March 26, 2021
Math Celebrity
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4 mod 3 ≡ 1 This means that 3 does not divide 4 → 3∤4
4 mod 3 ≡ 1 This means that 3 does not divide 4 → 3∤4
CalculatorSoup
calculatorsoup.com › calculators › math › modulo-calculator.php
Modulo Calculator
You can use the modulo calculation to accomplish this. If a number is a multiple of 4, when you divide it by 4 the remainder will be 0. So you would create the logic to take an input and use the mod 4 operation on it.
Khan Academy
khanacademy.org › computing › computer-science › cryptography › modarithmetic › a › what-is-modular-arithmetic
What is modular arithmetic? (article)
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Reddit
reddit.com › r/collatz › basic question: 1 mod 4
r/Collatz on Reddit: Basic Question: 1 mod 4
January 31, 2024 -
Basic question here.
For numbers that are congruent to 1 mod 4, it's pretty easy to show that these always end up at a smaller number in just three steps since the initial 3x+1 calculation always results in a multiple of 4. Does this mean that all numbers congruent to 1 mod 4 will end up in the 4-2-1 loop?
Example: 33 - 100 - 50 - 25
Top answer 1 of 5
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That they end up in a smaller number in three steps does not exclude the possibility of them getting bigger in the steps after that. You aren't guaranteed that after dividing by four you will get a number that is 1 mod 4.
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I think that the most that can be said is: the smallest number that doesn't converge to 1 must be 3mod4. The first 3 steps for a 1mod4 number: . 4n+1 -> 12n+4 -> 6n+2 -> 3n+1 and the last number is always smaller than the first number. So the "smallest number that doesn't converge to 1" can't be 1mod4 because 4n+1 goes to 3n+1, which is smaller and does converge to 1, which is a contradiction. So if there are numbers that don't converge to 1, the smallest of these must be 3mod4.
Quora
quora.com › What-is-3-mod-4
What is -3 mod 4? - Quora
So in this case the answer is remainder obtained when -3 is divided by 4. So 4 * -1 = -4 which is less than -3. So -1 is our quotient and we have -3 - (-4) as we subtract in division. Thus we get -3 + 4 = 1 which is our remainder. So -3 mod 4 is 1. ...
Visual Fractions
visualfractions.com › calculator › modulo › what-is-4-mod-3
What is 4 mod 3? (4 modulus 3)
We can see that multiples of 3 are 0, 3, 6, 9, etc. The highest multiple that is less than or equal to 4 is 3. So the final step in the modulus method here is to subtract the divisor highest multiple from the Dividend and answer the question "what is 4 modulus 3?":
Published March 26, 2021
YouTube
youtube.com › sybermath
Basics of Modular Arithmetic - YouTube
Join this channel to get access to perks:→ https://bit.ly/3cBgfR1 My merch → https://teespring.com/stores/sybermath?page=1Follow me → https://twitter.com/Syb...
Published May 3, 2021 Views 64K
Reddit
reddit.com › r/learnmath › when we talk about mod and reminder, what exactly are the reminders here, for example 3mod4 and -1mod4 how come the reminder is 3?
r/learnmath on Reddit: when we talk about mod and reminder, what exactly are the reminders here, for example 3mod4 and -1mod4 how come the reminder is 3?
June 10, 2023 -
when we talk about mod and reminder, what exactly are the reminders here, for example 3mod4 and -1mod4 how come the reminder is 3? is it about how much it left to reach the next integer number bigger integer or what, cuz for example here 3mod4 here is 3 so it's like it left only 1 to reach the next bigger integer the same for -1mod4?
Top answer 1 of 2
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For integers a and b, the remainder of division of a by b is the smallest non-negative integer r for which there exists an integer q such that a = qb + r.
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So, mod only works with integers, so you won't see fractional/decimal remainders. For 3mod4: How many times can 4 go into 3? Well, it won't fit, so 4 goes into 3 zero times. But we still have that 3 left over. the -1mod4 example works the same way.
How-To Geek
howtogeek.com › home › video games › 20 great games that are even better with mods
20 Great Games That Are Even Better With Mods
April 13, 2025 - Now, I don't know what you like, so your best bet is to go to Mod The Sims website, the primary source of The Sims mods, and browse The Sims mods to your heart's content. You can also check The Sims 3 and The Sims 4 pages on Nexus Mods.
Divisible Info
divisible.info › Modulo › What-is-3-mod-4.html
What is 3 mod 4? (3 modulo 4?) - Divisible
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 3 modulus 4 (3 mod 4): Multiples of 4 are 0, 4, 8, 12, etc. and the highest multiple of 4 equal to or less than 3 is 0. Therefore, to get the answer: 3 - 0 = 3 Thus, once again, the answer to "What is 3 mod ...
Divisible Info
divisible.info › Modulo › What-is-4-mod-3.html
What is 4 mod 3? (4 modulo 3?) - Divisible
Here is the math to illustrate how to get 4 mod 3 using our Modulo Method: 4 ÷ 3 ≈ 1.333333 1 × 3 = 3 4 - 3 = 1 Thus, the answer to "What is 4 mod 3?" is 1. Modulus Method To find 4 mod 3 using the Modulus Method, we first find the highest multiple of the Divisor (3) that is equal to or ...
Reddit
reddit.com › r/learnmath › how come -7 mod 3 is 2?
r/learnmath on Reddit: How come -7 mod 3 is 2?
June 19, 2024 -
I come from a computer science background and my mind is exploding rn from this.
In programming languages the % represents the modulo operation.
In most programming languages like C, Rust, Java, JavaScript -7 % 3 results in -1, this makes sense to me logically since if I have "negative 7 dollars" divided it across three people, each will get "-2 negative dollars" and "-1 negative dollar" will remain.
So how come in any calculators, and the few mathematics-friendly programming languages like Python and Haskell, -7 % 3 results in 2? Like logically speaking how could dividing a negative number result in a positive number, and where did the 2 even came from, from a logical standpoint?
Top answer 1 of 21
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Here’s a way to think about it that could help. In “mod 3”, each integer has to be in (exactly) one of three equivalency classes: 0, 1, or 2. You can list elements in each, keeping in mind that consecutive elements in each class are distanced from each other by the modulus (in this case, 3). The “0 class” contains { …, -9, -6, -3, 0, 3, 6, 9, … }. All elements in this set are equivalent to 0 mod 3. Each element can be achieved by starting at 0 and going up or down, counting by 3. The “1 class” contains { …, -8, -5, -2, 1, 4, 7, 10, … }. All elements in this set are equivalent to 1 mod 3. Each element can be achieved by starting at 1 and going up or down, counting by 3. The “2 class” contains { …, -7, -4, -1, 2, 5, 8, 11, … }. All elements in this set are equivalent to 2 mod 3. Each element can be achieved by starting at 2 and going up or down, counting by 3.
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How come -7 mod 3 is 2? For a, b ∈ ℤ, and n ∈ ℤ \ {0}, a ≡ b (mod n)means∃ q, r ∈ ℤ. a = qb + r. (Think ofqas the quotient, andr` as the remainder. They are not unique, so calling them "the quotient" and *"the remainder" is not strictly correct, but it's ok as an intuition. More on this below.) So, for what you're asking: -7 ≡ 2 (mod 3) because -7 = (-3)·3 + 2. But also: -7 ≡ -1 (mod 3) because -7 = (-1)·3 + 2. So, both -1 and 2 make perfect sense when it comes to picking out a result when you want to pick a representative for the congruence relation. Like logically speaking how could dividing a negative number result in a positive number, and where did the 2 even came from, from a logical standpoint? For a ∈ ℤ and b ∈ ℕ \ {0}, there exist unique q, r ∈ ℤ such that a = qb + r and 0 ≤ r < b. We say that q is the quotient and r is the remainder of division of a by b. (Note that we now do have uniqueness.) It is this definition of the remainder, which insists that the remainder has to be between 0 and the divisor, that's being used when setting -7 % 3 = 2 in programming languages that want their operands to be better aligned with commonly used mathematical definitions.
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