In Exercises 41 to 62, perform the modular arithmetic. 1. (9+15) mod 7 3. (5 +22) mod 8 2. (12+8) mod 5 4. (501) mod 15 6. (28+31) mod 4 8. (62 +21) mod 2 5. (42+35) mod 3 7. (37+45) mod 12

Q: Use Fermat's Little Theorem to find each value. Remember, x-1) =1 (mod p). Write your answer in…

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Q: (a) 55 mod 7. (b) –101 div 3.

A: (a) 55 mod 7  As 55 = 7•7+6 So that  55 mod 7 = 6 mod 7

Q: 5. Let a, b, c, and n be integers. Prove that if a = b (mod n) and c = d (mod n), then a − c = b -d…

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Q: Number 1 only

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Q: Nap Lajoie has a lifetime batting average of 0.338. Assume that Nap Lajoie came to bat officially…

A: Given : Nap Lajoie has a lifetime batting average of 0.338 and came to bat officially six times…

Q: Discrete Math: Find the largest negative value of x such that x = 2 mod 3, x = 3 mod 5, x = 2 mod 7.

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Q: Najabhai

A: The objective of the question is to find all integers n that satisfy the equation n² + 503 = 0 (mod…

Q: (-130 mod 20·265 mod 20) mod 20 ?   clear answer please

A: a mod b gives the remainder when a is divided by b That is we express it as a=b q+ r where r is the…

Q: Number theory TOP 3 ONLY!!!

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Q: USING MODULAR ARITHMETIC PERFORM THE FOLLOWING OPERATIONS    A).  (27 + 7) (mod 4)…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Using appropriate methods, reduce (i) 419 mod 47, (ii) 141-10156 mod 47, (iii) 483 mod 47, (iv) (419…

A: We have to reduce the following congruent equation.

Q: Jsing only definition of divisibility, definition of modulo, substitution, and arithmetic, prove for…

A: a ≡ b (mod m), c ≡ d (mod m) ⇒ m | a – b and m | c – d ⇒ m | ((a – b) + (c – d)) ⇒ m | ((a + c) – (b…

Q: Using the fast exponentiation method (page 182), determine 535 mod 47. Show your work.

A: We will find out the required value.

Q: O Find 5675 (mod 19

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Q: 9. Evaluate the expressions: a. 41 div 5= b. 41 mod 5= 9. Last Tuesday you agreed to meet a friend…

A: First we have evaluate expression-