Use Fermat’s little theorem to evaluate 9200 mod 19.

Q: Use the Chinese Remainder Theorem to find a solution to the congruences ´x = 2 mod 10 x = 3 mod 1001…

A: The given system is, x≡2mod10x≡3mod1001x≡3mod9 Chinese reminder theorem: If m1,m2,…,mn are positive…

Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: What is the remainder when 2021202120212021 is divided by 2020? use congruence modulo

A: a = 2021202120212021 b = 2020 If a = qb + r then  a ≡ r mod n.

Q: Use Fermat's little theorem to find the least residue of 8^70 modulo 23

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Use Eulers thm to find , 7଼8003 mod 1000

A:

Q: c) Using Fermat's Little Theorem, find 6142 mod 11.

A:

Q: Use Fermat's Little Theorem to compute 51990 mod 7.

A:

Q: Find the least positive inverse for 97 modulo 660.

A: Theorem used in the solution. For all integers a and b if gcd(a,b)=1 then there exists an integer s…

Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

A:

Q: Use the Fermat's Theorem to determine the last digit of 12347865435 when divided by 11

A:

Q: How to find 85307 (mod 739)?

A: To make it simple , divide power by 4 then solve .

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?.

A:

Q: Find a primitive root mod 131000

A: It is given that

Q: What is the least residue of 7162 modulo 17?

A: Multiplication rule for congruencesIf a ≡ b (mod n) and c ≡ d (mod n), thenac ≡ bd (mod n). Power…

Q: Show that every nonzero residue (mod 17) can be written as a power of 3

A:

Q: Find all the primitive roots modulo 125.

A:

Q: Find the remainder using Fermat’s Little theorem 452 mod 11.

A:

Q: The set {0,5,6} is closed under Mod(10)

A: To check if { 0 5, 6} is closed under mod(10)

Q: Prove that 2^10 + 5^12 is a composite number.

A:

Q: Determine a positive integer x such that 57x +7 = 78 (mod53).

A:

Q: 5. Use the method of successive squaring to compute 3875 (mod 103) 1

A:

Q: Find 1112 mod 13.

A:

Q: Use Fermat's theorem, show that if gcd(a, 145) = 1 then a141 = a (mod 145).

A:

Q: Find the inverse of 35 under mod 233(if exixts), by using Euclid's Algorithm?

A:

Q: Use Fermat's Little Theorem to find (Show work.) a) 945 mod.23. b) 231002 mod. 41 c) (-9)933 mod. 13

A: Fermat's Little theorem states that " if p is a prime number and a is not divisible by p then…

Q: Determine what number the product is congruent to in mod 3. 5.8 5.8 = (mod 3 )

A:

Q: Need Answer ASAP Using Fermat's Little Theorem to Calculate Each (Show Your Work) 1. 99 ^ 101 mod…

A:

Q: Use Fermat’s little theorem to find 231002 mod 41.

A:

Q: 122 is congruent to 5 modulo17 ?

A: To check whether -122 is congruent to 5 modulo 17 or not

Q: Show that 18! ≡ -1 (mod 437).

A: We have to show that: 18!≡-1mod437

Q: Find oll integers Such thot 24! x =1 Cmod 2) 5x = 3. (mod 8) and 1500 < X <2000

A:

Q: To Determine the value that 46 is congruent to IN modulo 7

A: Note that, If a and b are integers and n &gt; 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

A:

Q: Find inverse of 65 modulo 243

A: The definition of inverse modulo is: a is said to be the inverse of b modulo p, if ab≡1(mod p)

Q: Use Fermat's little theorem to find 231002 mod 13.

A:

Q: Using Fermat's theorem, find 3201 mod 11.

A: Euler's Theorem states that for any natural  number n, we  have  aϕ(n)≡1(mod n) where ϕ(n) denotes…

Q: Use Fermat's theorem to Reduce 50250 (mod 83) to a number in the range {0,1

A: Here we will find out the required value.

Q: Find a number that is less than 1740719 which is congruent to 577 modulo 1279 and congruent to 317…

A: Given, a number that is less than 1740719 which is congruent to 577 modulo 1279 and congruent to 317…

Q: Use Chinese theorem to find all positive integers that makes this congruence true:        x = 2 mod…

A:

Q: Then Find inverse of 21 mod 200.

A:

Q: Prove that no integer congruent to 3 modulo 4 can be written as the sum of two squares.

A:

Q: Use Euler's theorem to evaluate: 9 (mod 14) for a =1446.

A: Euler's theorem:- If gcd a,n=1 then aϕn≡1mod n. here ϕn is Euler's function. The number of integer…

Q: Show that if x mod 8 = 1, then (3x −5) mod 6 = 4.

A: Solution

Q: Find 2025-3 (mod 212). (Enter the least non-negative integer.)

A: To Find: 2025-3(mod 212) and enter the least non-negative integer.

Q: Use Fermat’s little theorem to find 7121 mod 13.

A:

Q: Use Fermat’s little theorem to find the least residue of 863 modulo 31.

A: Fermat's little theorem says: ap≡p(mod p)gcd(a,p)=1

Q: Find all the integers that satisfy 140x = 133 (mod 301).

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.