20. If a € Z and a = 1 (mod 5), then a² = 1 (mod 5). 23. Let a, b, c € Z and n EN. If a = b (mod n), then ca = cb (mod n).

Q: T F 5. To prove the statement: If ab =0 then a = 0 or b = 0, you may assume ab = 0 and a # 0 and…

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Q: 2. If x mod 5 = 4, then x could be O 571 O 400 O 633 O 719

A: Given               x(mod 5)=4

Q: 1. Let a, b, c, r, s, and t be integers with r>s>t>1. If a = b (mod r), a = c (mod s), and gcd(r,s)…

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Q: (c) For each integer a, if a 4 (mod 8), then a 2 (mod 8).

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Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

Q: If x mod 7 = 2, then x302 mod 7 is 04 02 D 1 05

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Q: 4. If x mod 7 = 3, then x27 mod 7 is O 3 0 6 O 5 O 4

A: Given :- x mod 7 = 3

Q: Prove that if a = b (mod m) and if c = d (mod m), then a+c=b+d (mod m).

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Q: For each pair of integers m and d, calculate m mod d. Show your work! a. m = 43 and d = 9 b. m 50…

A: If m and d be two integers . Then m mod d means that the remainder when m is divided by d .

Q: 9. Prove that if n = 3 (mod 4), then the equation x² + y² = n has no integer solution.

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Q: If A = 27 + 37 and B = 7+27, what is A + B ? c. a. 37 +5j b. 47+45 7+7 d. 57 +37

A: Given Vectors:- A→=2i+3j    and B→=i+2j

Q: 17. If 9x = 15 (mod 37), then x mod 37 is O 11 O 17 33 O 14

A: The given problem is to solve the given congruence equation. 9x = 15(mod 37).

Q: T T T F F F 11. 12. 13. If ab = 0 (mod 3), then a = 0 (mod 3) or b = 0 (mod 3). If ab = 0 (mod 6),…

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Q: 3. Suppose p = 2 (mod 5) and p is a prime number. Show that if x5 = 1 (mod p), then x = 1 (mod p).

A: We shall use basic modular arithmetic for solving this problem