Find the nonnegative integer a less than 28 represented by each of these pairs, where each pair represents (a mod 4, a mod 7).a) (0, 0) b) (1, 0) c) (1, 1)d) (2, 1) e) (2, 2) f ) (0, 3)g) (2, 0) h) (3, 5) i) (3, 6)

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Q: Assume that k mod 15 4. Compute 11k mod 15. Show all your work clearly.

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

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A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 21. How many positive integers x are there such that 3x has 3 digits and 4x has four digits?

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Q: 4. (a) Solve the set of congruences х 1(mod 3), x= 2(mod 4), x = 3(mod 5).

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Q: 25 Prove that mod 7 5 for all Gindegars and bin b mod 7-6

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Q: Q3/ Use Chinese theorem to solve the following congruence: X=2 mod 3 X=1 mod 5 X 2 mod 4

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Q: [Hint: It suffices to show that the numbe 11. Verify that 0, 1, 2, 2², 2³, . , 2° form a complete…

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Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

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