307 mod 730 using the techniques described in Example 8.4.4 and Example 8.4.5. Find 97 First compute the following. 97' mod 730 = 972 mod 730 = 974 mod 730 = 978 mod 730 = 9716 mod 730 = 9732 mod 730 = 9764 mod 730 = 97128 mod 730 = 974 ,256 mod 730 = Since 307 = 256 + 32 + 16 + 2 + 1, 97307 mod 730 = (97256 . 9732.97. 972 . 971)mod 730 (97256 mod 730) · (9732 = (97 mod 730) · mod 730)· (972 mod 730) · (97' mod 730) mod 730

Q: Find the following 122 (mod 35) 12 (mod 35) %3D 128 (mod 35) %3D 1216 (mod 35) %3D

A:

Q: Show that the permutations (12) and (12345) generate S5.

A: We have to show that the permutation 12 and 12345 generates S5. Suppose H=12,12345. We know that…

Q: Using the completed table, compute 8359 x 639 , but write the digits in reverse order (for example…

A: Given that, 8359 × 639 First multiply 8359 by unit digit of 639. Do the multiplication using the…

Q: Find the value of 592 (mod 11) using Fermat's Little Theorem. Remember, x (P-1) = 1 (mod p) a 592 =…

A:

Q: 4444 is divided by a 1.19) find the remainder when 4444 * 2?=-1 (mod a).

A: 1.19 We have 4444  ≡  7 (mod 9). So, 44444444 ≡ 7 4444 (mod 9) Now,       73 ≡1 (mod 9) Or,…

Q: Find 96307 7 (mod 739) using the techniques described in Example 8.4.4 and Example 8.4.5. First…

A: To find 96307mod739. It can be computed by evaluating the following,…

Q: In this whole worksheet, suppose n₁ = 3 and n₂ = 5. 1. Compute N = ₁+₂= Write out the list of…

A:

Q: 3. Find the following: A. 3^0 mod 5 1 B. 3^1 mod 5 3 C. 3^2 mod 5 1 D. 3^3 mod 5 4

A:

Q: 7. Calculate each of the following. [from #22, 4.5] b) 971321 (mod 765) a) 2557341 (mod 5681)

A:

Q: 7. Show that if n is odd, then p(4n) - 2 q(n). =

A: 7. Show that if n  is odd,then phi(4n)=2phi(n)

Q: Complete the following system: x = 5(mod 2) x = 6(mod 4)

A: Solve it.

Q: Apply the euler function if possible. 1212450(mod221) 1. 51211(тоd7) 2. 71350(mod12) 3.

A: By the Fermat's Little theorem: Let P is a prime number then for any integer a,  a∅p≡1modp Now,…

Q: Find the least residue of 448 modulo 7

A: Given problem is : Find the least residue of 448 modulo 7

Q: Find 74307 mod 724 using the techniques described in Example 8.4.4 and Example 8.4.5. First compute…

A:

Q: Compute σ0(1000), σ0(750), and σ0(1024)

A:

Q: Ans Encryt the message GO" by translating the letter, into number, applying the given encrytion…

A: We will use the basic knowledge of number theory and cryptography to answer this question completely…

Q: 1.16. Do the following modular computations. In each case, fill in the box with an integer between 0…

A: We have to calculate the following modulo.Note: According to the guidelines we are allowed to solve…

Q: mpute (278443 – 602430 * 123456) mod 20. Explain your work. -

A:

Q: a60 = a(mod 1001) a61 = a (mod 1001) This option This option

A:

Q: Use the method of Example 9.5.10 to answer the following questions. (a) How many 15-bit strings…

A:

Q: Calculate the remainder of 52021 (mod 39).

A: We have to calculate the remainder of 52021mod 39. We can write 52021mod 39=52020·5mod 39. We have…

Q: Use the EXTENDED EUCLIDEAN ALGORITHM to compute the following mul- tiplicative inverses: (a) 17-¹…

A: The extended Euclidean algorithm is an algorithm to compute the integers x and y such that for given…

Q: Find the smallest positive integer for which x mod 3 = 2 and a mod 4 = 3 What is the next smallest…

A:

Q: Let f(x) = sin (TT/6 sin (TT/2 sin x)) for all e R and g (x) =TT/2 sin x for all x e R. Let (fog)(x)…

A: Let f(x)=sinπ6sinπ2sinxg(x)=π2sin(x)

Q: Exercise 14.6.10. Prove that it is impossible to write the identity permu- tation as the product of…

A: We have to show it is impossible to write the identity permutation as the product of an odd number…

Q: Alice publishes her RSA public key: modulus N = 2038667 and exponent 3. ob wants to send Alice the…

A:

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

A:

Q: Compute 25200 mod 27.

A: As 25 is coprime to 27, by Euler's theorem, we see        25φ(27) ≡ 1 (mod 27)  Now,        φ(27) =…

Q: Activity 4.1 Directions: Prove or disprove the following statemen a short explanation of your step…

A:

Q: 1.21 Theorem. Let a natural number n be expressed in base 10 as  n=akak-1...a1a0 (Note that what we…

A: We know that 10 mod 3 = 1. So,

Q: Find the inverse to 2 by using the Euclid's algorithm  2 mod

A:

Q: Calculate 21212 (mod 9211), reducing it to a positive number less than 9211. Show your calculations.…

A: The objective of this question is to calculate the modulo of 21212 by 9211. The modulo operation,…

Q: Which of the following is the given permutation expressed as a product of disjoint cycles? * a =…

A: We have to solve through permutations group

Q: Find the inverse of 47 mod 30 or 47 x = 1 (mod 30)

A:

Q: Convert A2B3C4D516 to Xg. O 24245742325 O 24254472325 O 24254724325 O 24257442325 O 24245724425 O…

A:

Q: Compute 177121 mod 11.

A: To find 177121 = mod 11

Q: Compute 21200 mod 27.

A: We see,         21 ≡ (-6)  mod 27     => 212 ≡ (-6)2  mod 27                 ≡ 36  mod 27…

Q: Compute (1001 mod d) for d = 2, 3,..., 10.

A:

Q: Compute 21200 mod 27.

A:

Q: Let p= 29 and q = 31, and let e = = 101 %3D (a) Find n = pq and o(n). (b) Find d.

A: Since you have posted a question with multiple sub-parts, we will solve first few sub-parts for you.…