1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ksju [112]
3 years ago
10

Suppose that a, b \in \mathbb{Z}a,b∈Z, not both 00, and let d=\gcd(a, b)d=gcd(a,b). Bezout's theorem states that dd can be writt

en as a linear combination of aa and bb, that is, there exist integers m, n \in \mathbb{Z}m,n∈Z such that d = am + bnd=am+bn. Prove that, on the other hand, any linear combination of aa and bb is divisible by dd. That is, suppose that t = ax + byt=ax+by for some integers x, y \in \mathbb{Z}x,y∈Z. Prove that d \, | \, td∣t.
Mathematics
1 answer:
lara [203]3 years ago
3 0

Answer:

Step-by-step explanation:

Recall that we say that d | a if there exists an integer k for which a = dk. So, let d = gcd(a,b) and let x, y be integers. Let t = ax+by.

We know that d | a, d | b so there exists integers k,m such that a = kd and b = md. Then,

t = ax+by = (kd)x+(md)y = d(kx+my). Recall that since k,  x, m, y are integers, then (kx+my) is also an integer. This proves that d | t.

You might be interested in
Hi can you guys help me. The topic is similiar shapes in this case triangles do you guys know how to find a length. I got some p
Airida [17]

PR=18mm
AB=7mm

All lengths of triangle PRQ are twice the lengths of ACB





4 0
3 years ago
2(3x-7)=34 please help
IrinaK [193]

Answer:

x=8

Step-by-step explanation:

2*3x=6x

2*-7=-14

6x-14=34

6x+14=34+14

6x=48

6x/48

x=8

3 0
2 years ago
The mean length of 4 childrens' big finger is 14cm. The mean length of 9 adults' big finger is 16.1cm. What is the mean length (
Mamont248 [21]

Answer:

The mean length of the 13 people's big finger is 15.45 cm

Step-by-step explanation:

Given;

mean length of 4 childrens' big finger, x' = 14cm

mean length of 9 adults' big finger is 16.1cm, x'' = 16.1cm

Let the total length of the 4 childrens' big finger = t

x' = \frac{t}{n} \\\\x' = \frac{t}{4}\\\\t = 4x'\\\\t = 4 *14\\\\t = 56 \ cm

Let the total length of the 9 adults' big finger = T

x'' = \frac{T}{N} \\\\x'' = \frac{T}{9}\\\\T = 9x''\\\\T = 9*16.1\\\\T = 144.9 \ cm

The total length of the 13 people's big finger = t + T

                                                                           = 56 + 144.9

                                                                            =200.9 cm

The mean length of these 13 people's big finger;

x''' = (200.9) / 13

x''' = 15.4539 cm

x''' = 15.45 cm (2 DP)

Therefore, the mean length of the 13 people's big finger is 15.45 cm

3 0
3 years ago
Evaluate the equation 45,267-q=17,012
stich3 [128]
Q=28255 hope it helps ig
3 0
3 years ago
If you draw two cards from the deck at the same time, what is the probability that they will both be hearts?
koban [17]

Answer:

The probability is 1/17.

Step-by-step explanation:

The total number of ways in which 2 cards can be selected from a pack of 52 cards is \binom{52}{2}

The total number of combinations of 2 cards with hearts equals \binom{13}{2}

Thus the probability of the event that both the cards have hearts becomes

P(E)=\frac{\binom{13}{2}}{\binom{52}{2}}=\frac{1}{17}

4 0
2 years ago
Other questions:
  • HELP ASAP!!!
    6·2 answers
  • A Pudding recipe calls for 0.355 liter of milk. Nati has 0.5 liter of milk at home. Does she have enough milk for the pudding re
    11·1 answer
  • Albert's hourly pay is $8.10. He has an hourly pay of $12.15 when he works more than 40 hours. He worked 45 hours last week. Wha
    11·1 answer
  • A deep sea diver must descends below the surface of the water at a rate of 60 feet each minute. what is the depth of the diver a
    13·2 answers
  • Points
    13·1 answer
  • Solving for y what is 3x-4y=-8<br> solving for y what is 3x-4y=-8
    8·1 answer
  • Devon has 100 dimes and quarters. If the total value of what he has is $21.40, how many of each coin type does he have?
    8·2 answers
  • What is the value of the y-intercept of the graph of h(x) = 1.2(4.15)^x?
    14·1 answer
  • On Map 1, which has a scale of 1:25000, length of road is 5.5cm and the area of a park is 1.4cm2
    12·1 answer
  • Someone please explain how this make sense
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!