# modular arithmetic in a sentence

1) These proofs require some background in

**modular**

**arithmetic**.

arithmetic collocations

2) This makes use of

**modular**

**arithmetic**for provisions especially attractive.

3) In modern times

**modular**

**arithmetic**is sometimes used in Digital signal processing.

## modular **arithmetic** example sentences

4) He further advanced **modular**

**arithmetic**, greatly simplifying manipulations in number theory.

5)

**Modular**

**arithmetic**is convenient for calculating the check digit using modulus 11.

6)

**Modular**

**arithmetic**is often used to calculate checksums that are used within identifiers.

7) Why it is valid to "cancel" in the setting of

**modular**

**arithmetic**.

8) Standard properties of addition and multiplication familiar from the integers remain valid in

**modular**

**arithmetic**.

9) The notion of

**modular**

**arithmetic**is related to that of the remainder in Euclidean division.

10)

**Modular**

**arithmetic**, and in particular,

**modular**exponentiation , comes to the rescue.

11) In

**modular**

**arithmetic**, some numbers have a multiplicative inverse with respect to the modulus.

12) This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in

**modular**

**arithmetic**.

13) In this

**modular**art article, one can learn more about applications of

**modular**

**arithmetic**in art.

14) Another way to find a solution is with basic algebra,

**modular**

**arithmetic**, and stepwise substitution.

15) Another advantage of this convention is in the use of

**modular**

**arithmetic**as implemented in modern computers.

### example sentences with **modular** **arithmetic**

16) It is used in polynomial factorization, a problem for which all known efficient algorithms use **modular**

**arithmetic**.

17) The credit counters are

**modular**counters, and the comparison of consumed credits to credit limit requires

**modular**

**arithmetic**.

18) A great convenience of

**modular**

**arithmetic**is that it is easy to multiply, though quite difficult to add.

19) This is well defined because addition and multiplication commute with the "mod" operator; see

**modular**

**arithmetic**.

20) Article 16 of Gauss' "Disquisitiones Arithmeticae" is an early modern statement and proof employing

**modular**

**arithmetic**.

21) In all cases, addition and subtraction of subscripts should be performed using

**modular**

**arithmetic**with modulus "n".

22) Using number-theoretic transforms instead of discrete Fourier transforms avoids rounding error problems by using

**modular**

**arithmetic**instead of floating-point arithmetic.

23) In computer algebra,

**modular**

**arithmetics**is commonly used to limit the size of integer coefficients in intermediate calculations and data.

24) In computer science,

**modular**

**arithmetic**is often applied in bitwise operations and other operations involving fixed-width, cyclic data structures.

25) Interesting cases are finite fields and

**modular**

**arithmetics**, for which the article root of unity modulo n contains some information.

26) In

**modular**

**arithmetic**, two integers are added and then the sum is divided by a positive integer called the "modulus.

27) The distinctive feature of prime numbers is the following: division is possible in

**modular**

**arithmetic**if and only if n is a prime.

28) By avoiding

**modular**

**arithmetic**, this method is much easier to implement and also runs significantly faster in practice (usually by at least a factor of four).

#### How to use **modular** **arithmetic** in a sentence

29) For example, in **modular**

**arithmetic**, a finite group of size n can be formed by partitioning the integers via the equivalence relation x~y iff x=y(mod n).

30) The base step, that 0 "p" ≡ 0 (mod "p"), is true for

**modular**

**arithmetic**because it is true for integers.

31) This is a simple consequence of the laws of

**modular**

**arithmetic**; we are simply saying that we may first reduce "a" modulo "p".

32) In

**modular**

**arithmetic**, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory.

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