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3 years ago

8

✨✨Hiii'm new here can you tell me how to use this app? ❤❤FROM INDIA

2 answers:

Lyrx [107]3 years ago

7 0

Basically this app helps you with any question you need you got to ask a question and people will answer it for you just like i am doing now also you can answer other peoples questions to get points.

kow [346]3 years ago

6 0

of course. you may answer peoples' question and receive points which raises your status and whatnot. you can also ask questions of your own and receive helpful feedback.

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Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

2 years ago

For each sentence, write an equation.

Dafna11 [192]

A) x/6=9
Subtract 6 from both sides, x=3

B) x/-4=-3
Add 4 to both sides, x=1

C) x/-5=7
Add 5 to both sides, x=12

5 0

3 years ago

Write 5 over 15 in simplest form.

seraphim [82]

Answer: 1/3

Step-by-step explanation:

5/15 divided both by 5 is 1/3

5 0

3 years ago

The model below represents an equation.

Aleks04 [339]

Answer:

2 long x tiles and 3 long x tiles are like terms.

Step-by-step explanation:

6 0

3 years ago

Plz help ASAP I will mark u branliest

-BARSIC- [3]

Answer:

Brainliest?

Step-by-step explanation:

1.

subtract 1 from both sides

divide by 2

2.

add 5 to each side

divide by 4

6 0

3 years ago

Read 2 more answers