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Nadusha1986 [10]
3 years ago
8

Please help with this math work.

Mathematics
1 answer:
Musya8 [376]3 years ago
4 0
What is the questionnn
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WHAT IS THE REMAINDER WHEN <img src="https://tex.z-dn.net/?f=32%5E%7B37%5E%7B32%7D%20%7D" id="TexFormula1" title="32^{37^{32} }"
Feliz [49]

Recall Euler's theorem: if \gcd(a,n) = 1, then

a^{\phi(n)} \equiv 1 \pmod n

where \phi is Euler's totient function.

We have \gcd(9,32) = 1 - in fact, \gcd(9,32^k)=1 for any k\in\Bbb N since 9=3^2 and 32=2^5 share no common divisors - as well as \phi(9) = 6.

Now,

37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} =  32\cdot\left(32^{(\cdots)}\right)^6

where the c_i are positive integer coefficients from the binomial expansion. By Euler's theorem,

\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9

so that

32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9

7 0
2 years ago
What is the equation of a line that passes through the point (-4, 3) and has a slope of 1/2 ?
AysviL [449]

Answer:

y = 1/2x + 5

sorry no explanation but pls give brainliest

3 0
3 years ago
Express 84,42 as a percentage of 74,05 rounded off to a whole number
Leto [7]
0.84, 0.42, 75 AND 5

5 0
3 years ago
contestants in a dance-a-thon rest for the same amount of time every hour.a couple rests for 25 minutes in 5 hours.how long did
vladimir1956 [14]

Answer

Find out the how long did they rest in 8 hours.

To prove

As given

contestants in a dance-a-thon rest for the same amount of time every hour.

A couple rests for 25 minutes in 5 hours .

As

25 mintues = 5 hours

1\ hours = \frac{25}{5}\ mintues

1 hours = 5 mintues

Thus in 1hours a the dance -a-thon rest for 5 mintues.

Now for 8 hours.

8 hours = 8 × 5 mintues

           = 40 mintues

Therefore in 8 hours  a dance-a-thon rest for 40 mintues.




3 0
3 years ago
Read 2 more answers
A family eats at a restaurant . The bill is$ 42 dollars . The family leaves a tip and spends $ 49.77 dollars .
bagirrra123 [75]

Answer:

Since you didnt include an actual question im guessing you are looking for the tip amount which would be $ 7.77

Step-by-step explanation:

49.77-42=7.77

3 0
3 years ago
Read 2 more answers
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