Consider p> 2 a prime number, justify that: (P,') = (-1)" (mod p) to any 0 sn sp- 1,n EN. 1.1 1.2 (P)= 0 (mod p) to any natural number 2snsp- 1. (2p = 2 (mod p). Suggestion: Use paragraph 1.1 and 1.2 1.3

Q: Prove this claim: For every positive integer d and every integer n, the following equation is…

A: Using division algorithm we solve this problem. The steps are given bellow.

Q: Fn+1 Fr-1 Show that A"; 3. Let Fn denote the nth Fibonacci number. Let A = (Hint: use induction).

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Q: Let n = 17. Sha

A: Given: Value of a, b, n. We have to check whether a≡b mod n    or   a≢b mod n.

Q: The remainder when a is divided by 7 is 2 and the remainder when b is divided by 7 is 5. (So a mod 7…

A: Given that remainder when "a" is divided by 7 is 2

Q: Suppose that a and b are integers such that a = 45 (mod 71) and b = 53 (mod 71). Find an integer c…

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Q: Find the residue for the following case. 86 (mod 7) The residue of 86 (mod 7) is (Round to the…

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Q: a) Prove that 10" =+1 (mod 11) for any n EN. b) Suppose the integer r has digits rI-1I, I0. Prove…

A: Want to prove:(a) 10n≡±1 (mod 11) for any n∈N(b) If the integer x has digits xnxn-1.....x1x0 thenx≡0…

Q: Prove the assertions below: (a) If a is an odd integer, then a? = 1 (mod 8). (b) For any integer a,…

A: In this question, we have given assertion in terms of congruence modulo here we prove  8(a) if a is…

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

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Q: For which primes p > 5 is -5 a square mod p? Your answer should be of the formp = {a1, a2, ..., ak}…

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Q: He have to Show that lon = (-1)" (mod 1") shall use mathematical moluction Let Pin) := lon a (47"…

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Q: 3. Show that ifn = 2 (mod 4), then 9" + 8" is divisible by 5.

A: Here we will prove the given statement.

Q: (a) Show that, for any odd prime p > 5, 1 if p = 1, –5 (mod 12) (주) -1 if p= -1,5 (mod 12)

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Q: If x98 = 1(mod 97) then possible value of x is of (a) 97 (b) 194 (c) 90 (d) 291 (е) None of these O…

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Q: 157" =x (mod 11), 0 <x<11

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Q: 9 The residue of 6 (mod 5) is (Round to the nearest whole number.)

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Q: Determine the cube root of (3 + j4). ound-off the modulus to 3 decimal places, the angle to the…

A: Cube root of (3+4j)

Q: (18)280 mod 125 =

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Q: 5. Prove or disprove the following proposition: Let the Jacobi symbol: =1. %3D Then a is quadratic…

A: The complete solutions are given below

Q: Find an integer A so that: A79 = 7 (mod 277) Please solve step by step thanks!

A: Given an equation. Let's solve for A.

Q: ) If 112021 =r (mod 13), Find out the value of r. Justify the answer with your work.

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Q: If x00 = 1(mod 109) then possible value of x is a) 108 (b) 218 (c) 109 (d) None of these

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Q: Recall the Fibonacci numbers Fn are defined by Fo = 0 , F1 = 1 and Fn Fn-1 + Fn-2 for all n > 2 .…

A: Consider the provided question, Fibonacci numbers Fn are defined by F0=0, F1=1 and Fn= Fn-1+Fn-2 for…

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

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Q: 2.) Find the check digit (d) for the UPC numbers 0-32692-03012 d

A: 2. The given UPC number is 0-32692-03012-d. We use the first 11 digits 0-32692-03012 to determine…

Q: Evaluate the following: 495 (mod 11) 3(mod 8) 2345(mod 6) (i) (ii) (iii) 9

A: As per bartleby guidelines we only give first three questions answers. Please repost for other…

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

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Q: Let p > 3 be a prime. Show that if p2+ p + 1 is also prime, then p =5 mod 6.

A: We prove the result by the method of contradiction.

Q: Find the modulus and argument of 5 - 7i.

A: Since the modulus of a complex number a+ib is |a+ib|=a2+b2. So, the modulus of 5-7i is…

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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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: 20.What is the value of n such that (24  is congruent to 58 mod n) ? a.13 b.17 c.-34 d.-13

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Find the ones 171 22 digit of n=11 +3 +|

A: We need to determine the ones digit of the expression: 11171+322+1. We need to determine the ones…

Q: Find a such that 5= 7* modulo 13.

A: Given: 5≡7xmodulo13. The objective is to find the value of x.

Q: 1. i) Explain why 3 is a primitive root modulo 14 ii) What is log3(11) mod 14?

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Q: Evaluate the expressions. (a) 50 div 7 7.143 (b) 50 mod 7 1 ]x

A: We shall answer the following in next step. We also recall the definitions

Q: Please write neatly and provide all the necessary steps for solving If p is an odd prime prove that…

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