Understanding Modular Inverses

What is the range of integers considered in mod 392?

• 1 to 391

• 0 to 391

• 1 to 392

• 0 to 392

What is the goal when finding the inverse of a number in modular arithmetic?

• To find a number that subtracts to one

• To find a number that adds to zero

• To find a number that divides to zero

• To find a number that multiplies to one

What is the first step in applying the Euclidean algorithm to find the inverse of 27 mod 392?

• Subtract 27 from 392

• Divide 27 by 392

• Express 392 as a multiple of 27 plus a remainder

• Express 27 as a multiple of 392 plus a remainder

In the Euclidean algorithm, what is the remainder when 392 is divided by 27?

• 13

• 14

• 392

• 27

What is the next step after expressing 27 as 14 * 1 + 13 in the Euclidean algorithm?

• Express 13 as a multiple of 14

• Express 392 as a multiple of 13

• Express 14 as a multiple of 13

• Express 27 as a multiple of 13

What is the purpose of substituting equations in the Euclidean algorithm?

• To find the greatest common divisor

• To simplify the equations

• To eliminate variables

• To express the inverse in terms of known values

How is the negative value -29 converted to a positive equivalent in mod 392?

• By dividing 29 by 392

• By multiplying 29 by 392

• By subtracting 29 from 392

• By adding 29 to 392

What is the final inverse of 27 mod 392?

• 1

• 363

• 392

• 27

Why does the term 2 * 392 become zero in mod 392?

• Because 2 is a factor of 392

• Because 392 is the inverse of 2

• Because 392 is a prime number

• Because any number times 392 is zero in mod 392

What is the significance of the result 27 * 363 = 1 mod 392?

• It indicates that 27 and 363 are coprime

• It proves that 392 is a multiple of 27

• It confirms that 363 is the inverse of 27 mod 392

• It shows that 27 is a prime number