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3 modulo 5 =

3

calculatorsoup.com › calculators › math › modulo-calculator.php

If you did not use the mod operator you would have to do the math in your code. For example you would have to calculate "is 496 a multiple of 4?". You would divide 496 by 4, so 496 / 4 = 124 with no remainder.

Quora

quora.com › What-is-3mod5

What is 3mod5? - Quora

Answer (1 of 3): In software, “mod” tends to be used as a binary operation, where “m \mod n" is the remainder when m is divided by n. (There are different rules for what to do when either m or n is negative, depending on which environment one is in. At my job we use both C++ and Python, ...

Stack Exchange

math.stackexchange.com › questions › 194629 › how-is-3-equiv-3-bmod5

modular arithmetic - How is $3\equiv 3\bmod{5}$ - Mathematics Stack Exchange

Top answer

1 of 6

15

If $\text{[math]}$ and $\text{[math]}$ are positive integers, there exist unique integers $\text{[math]}$ , $\text{[math]}$ with $\text{[math]}$ and $\text{[math]}$ .

This theorem is called the division algorithm, and $\text{[math]}$ is defined to be this $\text{[math]}$ . In your case, $\text{[math]}$ and $\text{[math]}$ , so the answer is 3.

2 of 6

3

$\text{[math]}$ means $\text{[math]}$ is divisible by $\text{[math]}$ . [Definition]

Since $\text{[math]}$ is divisible by $\text{[math]}$ , we have $\text{[math]}$ .

Discussions

Why is -5 mod 3 = 1 and not 2?

Because -5+2(3)=1. But 2=-5+7, and 7 isn't a multiple of 3. In general, negatives and positives need not be congruent in modular arithmetic. 5 and -5 are 10 apart, so -5 ≢ 5 mod 3. More on reddit.com

r/learnmath

13

9

December 7, 2016

what is mod?

n (mod m) is just the remainder you get when divide n by m. So for example, take 27 (mod 5). When you divide 27 by 5, you have 2 remaining ( because 27 = 5 * 5 + 2). That's really all it is, it gives you the integer remainder of a number divided by m. If you write out some examples you'll see why it cycles: 0 = 0 * 5 + 0 [0 mod 5 = 0] 1 = 0 * 5 + 1 [1 mod 5 = 1] 2 = 0 * 5 + 2 [2 mod 5 = 2] 3 = 0 * 5 + 3 [3 mod 5 = 3] 4 = 0 * 5 + 4 [4 mod 5 = 4] 5 = 1 * 5 + 0 [5 mod 5 = 0] 6 = 1 * 5 + 1 [6 mod 5 = 1] 7 = 1 * 5 + 2 [7 mod 5 = 2] 8 = 1 * 5 + 3 [8 mod 5 = 3] 9 = 1 * 5 + 4 [9 mod 5 = 4] ... You may also hear than a = b (mod n) if (b - a) is a multiple of n. But this is just because if a and b are equal (mod n) then they have to have the same remainder r, so a = nx + r and b = ny + r, but then b - a = n(y - x) as stated above. More on reddit.com

r/learnmath

8

1

April 27, 2023

elementary number theory - Mod question: $-5 \pmod 3$? - Mathematics Stack Exchange

Alternatively, simply note that $$-5 = 1 + 3 \cdot -2 \implies -5 = 1\pmod{3}.$$ ... The other answers already give you enough ways to get to $5\equiv -1\equiv 2 ~(\operatorname{mod}3) $, I just want to say something about your notation. More on math.stackexchange.com

math.stackexchange.com

July 16, 2015

Understanding The Modulus Operator % - Stack Overflow

You may not have learned modular arithmetic, but you have probably used angles and know that -90° is the same as 270° because it is modulo 360. It's similar, it wraps! So take a circle, and say that its perimeter is 7. Then you read where is 5. And if you try with 10, it should be at 3 because ... More on stackoverflow.com

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