It can be shown that every integer can be uniquely represented in the form ek1341 where e=-1, 0, or 1 for j 0, 1, 2,. . ., k. Expansions of this type are called balanced ternary expansions. Find the balanced temary expansions of 11 .+ ej3 + eo, ...

Q: The coefficient of x6y12 in the expansion of (x + y)18 is ___________.

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Q: 7. Use Pascal's Triangle to expand the binomial (2x + 2)¹. O 16x¹64x³ +96x² - 64x + 16 - 16x4 + 64x³…

A: To expand using the Pascal triangle.

Q: Convert the sum of (ABC19)16 and (19ABC)16 into its binary expansion

A: The given numbers are                                          ABC1916  and  19ABC16 Here we have to…

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

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Q: 9. Prove that n - n is divisible by 30 for every integer n. te

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Q: 48. A student made the following statements regarding the expansion of (a + b)* written in…

A: We have to expansion (a+b)4 written in descending powers of a and say that for this given statements…

Q: 3. Which of the following integers are divisible by 3? Of those that are, which are divisible by 9?…

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Q: 4. Suppose that a positive integer is written in decimal notation as n = akak-1 a2a1ao where 0 <a;…

A: Here, we use theory of congruences.

Q: 14. Prove that 32n +7 is divisible by 8. 15. Prove that 7"-2" is divisible by 5. 16. Prove that n³ -…

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Q: How many 12-bit strings (that is, bit strings of length 12) are there which: a. Start with the…

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Q: Let n (arak-1 ·*a1a0)3 be the base 3 expansion of a positive integer n. Find the base 3 expansion of…

A: Solution: We know that if for any positive integer r have the base 3 expansion (ap,ap-1,.....,a0)3…

Q: Decide whether the following binomial congruence has any solutions x2" = 10 mod 103. Use modular…

A: We have to decide whether the following binomial congruence has any solutions or not.…

Q: Secton 5.1 Excerciser # 4

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Q: 2. Find the fourth term of the expansion of (a + 2b)¹0 without writing out the entire expansion.

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Q: 3. Convert the decimal expansion of (231)10 to a binary expansion a) (1100111), b) (1110011)2 c)…

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Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b)…

A: Given: (101111110)2 (1010000011)2 (111000000)2 (1011011101)2 Which of these is divisible by 3

Q: 9. Prove that n is odd, then n² - 1 is divisible by 8.

A: In this question, we will prove the question.

Q: The binary expansion 0.abcd... means 23 24 and each binary digit a, b, c, d, ... is either 0 or 1.…

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