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
Artist 52 [7]
2 years ago
7

Use strong mathematical induction to prove the existence part of the unique factorization of integers theorem (Theorem 4.4.5). I

n other words, prove that every integer greater than 1 is either a prime number or a product of prime numbers.
Mathematics
1 answer:
valentina_108 [34]2 years ago
5 0

Answer:

Lets say that P(n) is true if n is a prime or a product of prime numbers. We want to show that P(n) is true for all n > 1.

The base case is n=2. P(2) is true because 2 is prime.

Now lets use the inductive hypothesis. Lets take a number n > 2, and we will assume that P(k) is true for any integer k such that 1 < k < n. We want to show that P(n) is true. We may assume that n is not prime, otherwise, P(n) would be trivially true. Since n is not prime, there exist positive integers a,b greater than 1 such that a*b = n. Note that 1 < a < n and 1 < b < n, thus P(a) and P(b) are true. Therefore there exists primes p1, ...., pj and pj+1, ..., pl such that

p1*p2*...*pj = a

pj+1*pj+2*...*pl = b

As a result

n = a*b = (p1*......*pj)*(pj+1*....*pl) = p1*....*pj*....pl

Since we could write n as a product of primes, then P(n) is also true. For strong induction, we conclude than P(n) is true for all integers greater than 1.

You might be interested in
9/6 as an equivalent fraction
svet-max [94.6K]
3/2 We look for a number that goes into both 9 and 6 without leaving a remainder, and that number is 3
3 0
3 years ago
What is 37.5 percent of 80
Leya [2.2K]
37.5*0.010=.375 (or press % button on calculator) 
80*.375=30 
7 0
3 years ago
16.4.57 Question Help A box contains eighteen $1 bills, ten $5 bills, eight $10 bills, three $20 bills, and one $100 bill You bl
Rudiy27

Answer:

$ 7.7

Step-by-step explanation:

Given,

There are 18 $1 bills, ten $5 bills, eight $10 bills, three $20 bills, and one $100 bill,

Total number of bills = 18 + 10 + 8 + 3 + 1 = 40,

\because \text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}

Thus,

The probability of $ 1 = \frac{18}{40}

The probability of $ 5 = \frac{10}{40}

The probability of $ 10 = \frac{8}{40}

The probability of $ 20 = \frac{3}{40}

The probability of $ 100 = \frac{1}{40}

If a bill is selected randomly,

The expected value of the bill

=\frac{18}{40}\times 1+\frac{10}{40}\times 5+\frac{8}{40}\times 10+\frac{3}{40}\times 20+\frac{1}{40}\times 100

=\frac{18+50+80+60+100}{40}

=\frac{308}{40}

= $ 7.7

5 0
2 years ago
Is -2(-3) a positive or negative answer???
Natalija [7]

Answer: positive

Step-by-step explanation: it’s positive because if you multiply two negative numbers they cancel each other out and it makes a positive number

5 0
3 years ago
Read 2 more answers
HELP!!!
Jlenok [28]
You can compose, or create, a parallelogram (a four-sided shape with two sets of opposite, parallel sides) using two shapes, such as triangles or squares. You can decompose, or take apart, a parallelogram by dividing it from opposite corners, either vertically or horizontally.
6 0
2 years ago
Other questions:
  • What is the answer of 7 copies of the sum of 8/5 + 4
    15·1 answer
  • Simplify...... <br> (U^2)^3
    11·1 answer
  • The original height of the leaning tower of pisa was 184.5 feet. at a distance of 140 feet from the base of the tower, the angle
    13·1 answer
  • 78 divided by 48 what is it between
    5·2 answers
  • Aiden has a collection of 63 nickels and quarters in his piggy bank. If the total value of the coins is $10.75, how many nickels
    15·1 answer
  • Mike jogged 6 laps around a 0.25 mile track on Monday and 7 laps on Tuesday. How many miles did he jog on Monday and Tuesday com
    11·2 answers
  • critically discuss how Fraud and corruption may negatively impact economic growth and development of a country ​
    11·1 answer
  • Can someone please help will mark brainlist
    8·1 answer
  • The table show the number of tubs of popcorn that a popcorn vendor sold at the baseball games for each month during baseball sea
    9·1 answer
  • The roots of x+1/x=3 are: (x not equal to 0)​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!