# Modulo arithmetic

This optimization is not possible for languages in which the result of the modulo operation has the sign of the dividend including C Modulo arithmetic, unless the dividend is of an unsigned integer type.

For all congruent numbers 2 and 14adding and subtracting has the same result. Play the mod N mini-game! As your hash table grows in size, you can recompute the modulo for the keys. Equivalencies[ edit ] Some modulo operations can be factored or expanded similarly to other mathematical operations.

For special cases, on some hardware, faster alternatives exist. You want to divide them into 2 groups. Give people numbers 0, 1, 2, and 3.

This is a bit more involved than a plain modulo operator, but the principle is the same. This can allow writing clearer code without compromising performance.

Add them up and divide by 4 — whoever gets the remainder exactly goes first. This is huge — it lets us explore math at a deeper level and find relationships between types of numbers, not specific ones. What about the number 3? We have 4 people playing a game and need to pick someone to go first.

Thus, the sign of the remainder is chosen to be nearest to zero. Odd, Even and Threeven Shortly after discovering whole numbers 1, 2, 3, 4, 5… we realized they fall into two groups: See the above link for more rigorous proofs — these are my intuitive pencil lines. Despite its widespread use, truncated division is shown to be inferior to the other definitions.

We do this reasoning intuitively, and in math terms: You have a flight arriving at 3pm. What do you do? For the mod m notation, see congruence relation. So it must be 2. For example, we can make rules like this: Some calculators have a mod function button, and many programming languages have a similar function, expressed as mod a, nfor example.An introduction to the notation and uses of modular arithmetic.

The best way to introduce modular arithmetic is to think of the face of a clock. A reader recently suggested I write about modular arithmetic (aka “taking the remainder”).

I hadn’t given it much thought, but realized the modulo is extremely powerful: it should be in our mental toolbox next to addition and multiplication. Instead of. The same is true in any other modulus (modular arithmetic system).

In modulo, we count. We can also count backwards in modulo 5.

Any time we subtract 1 from 0, we get 4. So, the integers from to, when written in modulo 5, are where is the same as in modulo 5. Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, Modulo arithmetic "wrap around" upon reaching a given fixed quantity, which is known as the modulus (which would be 12 in the case of hours on a clock, or 60 in the case of minutes or seconds on a clock).

Formally, modular. In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus). Given two positive numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n.