Formally prove that log(n!) = O(n log n).
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A: We will write as a linear combination of the vectors
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A: this basically states the following that any 2 cyclic groups of the same order are isomorphic.
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Q: elaborate
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A: We shall be using the fact that a^p-1 =1 mod p
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Q: can this please be written on paper pleaseee
A: To write the answer on paper.
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Q: theorem
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A: If gcd(a,p)=1 then ap−1≡1(modp)
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Q: 9. y = ln (3x - 5)
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Q: Find a root of f(x)=In(x²+1)-4 sin(x-1) with 10-3 accuracy.
A: f(x)=ln(x2+1)−4sin(x−1)Derivative with respect to xf′(x)=2xx2+1−4cos(x−1)Now…
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Q: 2. Let n₁,..., nk be pairwise relatively prime positive integers, and let n = n₁ ... nk. Recall we…
A: this is also famous known as the chinese remainder theorem
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Q: 1. Given that Pn(x) flrol+flro, z1](z-ro) + a₂(x-xo)(x-T₁) +as(x − To) (x − x₁)(x − x₂) + ......+ an…
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Q: = e. Convert from multiplicative to additive notation: (1) a²b³; (2) a=²(b=¹c)² =
A: Here we have to convert the multiplicative notation to additive notation of1) a2 (2) a-2(b-1c)2…
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Q: -10 X = a+ 10 2,0 -10 Write x as a linear combination of a and b. 2.0 b. 18 Hint: The preview shows…
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please show each step in detail. please give full comprehensive answer!! and provide the background needed
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