Question

Please answer in FULL detail!!

Prove that the Mobius function is NOT
**Completely** Multiplicative. Where completely
multiplicative is μ(m*n) = μ(m) * μ(n).

Answer #1

Answer in FULL detail both proofs please!
Prove if 5 | Fn then 5 | n.
and then Prove
If 5 | n then 5 | Fn. Where Fn is the Fibonacci Numbers.

Please prove the following statement, in FULL detail. (by the if
and only if proving technique, not induction!)
Prove that 5 | Un if and only if 5|n. Where Un is the Fibonacci
sequence.

Please answer the following completely, clearly, and neatly.
Thank you.
The multiplicative group Un is cyclic. The cyclic
generators for Un are called primitive nth
roots of unity. How many of the 20th roots of unity in
U20 are primitive, and why?

Please solve the following in FULL detail.
Using Un2 + (-1)n =
Un-1 * Un+1 to be true, Prove that any two
consecutive Fibonacci numbers are coprime.

Please answer the following in FULL detail!
Is there a Pythagorean triple consisting of three Fibonacci
numbers? Give an example if there is one, or a proof if there
isn't.

Multiplicative Principle (in terms of sets): If X and Y are
ﬁnite sets, then |X ×Y| = |X||Y|. D) You are going to give a
careful proof of the multiplicative principle, as broken up into
two steps:
(i) Find a bijection
φ : <m + n>→<m>×<n> for any pair of natural
numbers m and n. Note that you must describe explicitly a function
and show it is a bijection.
(ii) Give a careful proof of the multiplicative principle by
explaining...

Multiplicative Principle (in terms of sets): If X and Y are
ﬁnite sets, then |X ×Y| = |X||Y|.
D) You are going to give a careful proof of the multiplicative
principle, as broken up into two steps:
(i) Find a bijection
φ : <mn> → <m> × <n>
for any pair of natural numbers m and n. Note that you must
describe explicitly a function and show it is a bijection.
(ii) Give a careful proof of the multiplicative principle...

Prove that at a completely full Milwaukee Bucks game at the
Fiserv Forum, there must be at least two people that have
both the same birthday and the same first initial. (Note:
The fiserv forum has a capacity of about 17,500 people)

Prove that Q is infinite.
Please answer questions in clear hand-writing and show me the
full process, thank you so much (Sometimes I get the answer which
was difficult to read).

Number Theory Course , I need a full explained answer for those
proofs please
1. Prove that for every integer x, x + 4 is odd if and only if x
+ 7 is even.
2. Prove that for every integer x, if x is odd then there exists an
integer y such that x^2 = 8y + 1.

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