Find all solutions of the congmonce 12X = 3 (mod 45)

Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: quadratic equation r2 + 4x-3 0 have a solution modulo 41"

A:

Q: We know that x^2= 2(mod 112) and try to find the solution of x

A: This is a problem of Number Theory.

Q: Solve y² = 37(mod 77)

A: We have to find the value of y  Using quadratic reciprocity property we find value of y

Q: How many 10 digit real even number can be created (It cannot start with a 0) with 5 zeroes and 5…

A: Basic concepts of making combination are used. Information given, As we have only two choices of…

Q: 4x=22(mod10)

A:

Q: Solve the following quadratic equation via the two different methods namely both classical and…

A: The equation a≡b mod n means that a-b is divisible by n. That is, the remainder when a-b is divided…

Q: + 220 + 330 + 440 + 550 + 660 (

A:

Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

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Q: Fill in the following blanks. Suppose you are finding 15^-1 (mod 131). This problem is equivalent to…

A: Answer follows

Q: The sum of the squares of the first 5 fibonacci terms, check and prove

A: Fibonnaci Sequence is: 1,1,2,3,5,8,13,21,34,55,89,... (That is, each term of the sequence is the sum…

Q: 12 = -3 (mod 5) Select one: True False

A:

Q: Find all solutions for x, up to congruence 7^78 (mod 79)

A:

Q: -3x = 4{mod8}

A: 3x = 4 (mod 8)  We have to find all integral value of x.

Q: If n is a positive integer prove that 3^(2n) - 26n -1 is divisible by 676

A: if n is a postive integer prove that 3^(2n) - 26n -1 is divisible  by 676

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: n)+3<10

A:

Q: True or False: 3^208= 3 mod 53.

A:

Q: Please explain how to solve: (5 · 17) (mod 8)

A: To solve  (5*17) (mod8) we use the properties of modulo

Q: solve for x^2 = 1 mod 8 and x^2 = 1 mod 10

A: Solution...

Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: Solve the equation 5x = 13 (mod 18)

A: Given: To solve: the equation 5x4≡13mod 18Formula: a≡bmod cis equivalent to saying by Euclid's…

Q: Find all integer solutions to 105x+343y=35 Using Magic Box | Elementary Number Theory

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Q: Show that this number is Irrational number

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Q: Solve the polynomial congruence x^3 - 3x^2 + 27 = 0 (mod 225). Please be detailed! I’m really…

A: Solution are fully explained in below steps Explanation:

Q: System of congruences (smallest +integer for answer): x = 3(mod 7) x = 4(mod 9) x = (1 mod 6)

A:

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT How many positive integers n ≤ 1000 are coprime with N=90

A: We know that 90=2×32×5 Numbers less than 1000 which are divisible by 2 =10002=500 Numbers less than…

Q: Use Hensel’s Lemma and Chinese Remainder Theorem to find all solutions to x^2 + 3x + 17 ≡0 (mod 300)

A: Introduction: Hensel’s Lemma is a powerful tool in number theory that allows us to lift solutions of…

Q: Prove that a1 + a2 = b₁ + b₂ mod n.

A: We have to prove that a1+a2=b1+b2 (mod n).Given:a1≡b1 (mod n)a2≡b2 (mod n)This means there exist…

Q: Solve 10x = 13 (mod 53)

A:

Q: Use your work from problem 2 and the method used in the example at the end of Lecture 16 to solve…

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Q: How many zeroes does 188! end with?

A: count number of five's in 188, 5*2=10 . Divide 188 and write quotient again divide quotient again by…

Q: How many integer solutions to x1+ x2+ x3+ x4 = 36 are there for which æ1 > 5, x2 > 3, x3 > 5 and æ4…

A: We have to find the number of solutions to x1+x2+x3+x4=36 for which x1≥5, x2≥3, x3≥5 &amp; x4≥6.

Q: Find all solutions of x = 10 (mod 133).

A: A congruence of the form, f(x)≡0(modm), where f(x)=anxn+an-1xn-1+...+a1x+a0, ai=0,1,2,...,n is…

Q: 9. Find all the solutions of 3x² + 2x + 1 8 (mod 63).

A: