Modular Arithmetic and Mathematica

What is the main idea behind modular arithmetic?

• Using only negative integers

• Using only positive integers

• Arranging integers on a circle

• Arranging integers on a straight line

In modular arithmetic, what is the result of 4 + 5 mod 7?

• 4

• 2

• 1

• 3

Which operator is commonly used for modulus in programming languages?

• @

• #

• %

• &

How can you compute the modulus of a negative integer?

• By subtracting the modulus

• By adding the modulus repeatedly

• By multiplying by the modulus

• By dividing by zero

What theorem provides a shortcut for modular exponentiation with a prime modulus?

• Gauss's Theorem

• Newton's Theorem

• Fermat's Little Theorem

• Pythagorean Theorem

What function in Mathematica is used for fast modular exponentiation?

• FastMod

• ExpMod

• PowerMod

• Mod

What is the multiplicative inverse of 5 mod 101?

• 20

• 81

• 50

• 25

Which Mathematica function can solve modular equations?

• Solve

• EquationMod

• RootSolve

• ModSolve

What function reduces polynomial coefficients to a specified modulus in Mathematica?

• PolyMod

• CoeffMod

• ReduceMod

• PolynomialMod

What is Euler's totient function used for in modular arithmetic?

• Determining the prime factors of a number

• Solving quadratic equations

• Calculating the number of integers less than n that are coprime to n

• Finding the greatest common divisor