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Prime Numbers and Composite Numbers

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Đỗ Phi Phi
26/07/2017 at 21:39
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A prime number is called a jillyprime when doubling it and adding 1 results in another prime. How many numbers lass than 15 are jillyprimes? (Note that 1 is not a prime.)

Prime Numbers and Composite Numbersdouble countingadding

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    Phan Thanh Tinh Coordinator 26/07/2017 at 23:34

    2 x 2 + 1 = 5

    3 x 2 + 1 = 7

    5 x 2 + 1 = 11

    7 x 2 + 1 = 15

    11 x 2 + 1 = 23

    13 x 2 + 1 = 27

    So,there are 4 jillyprimes which are less than 15 : 2 ; 3 ; 5 ; 11 

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  • ...
    FA KAKALOTS 28/01/2018 at 22:04

    2 x 2 + 1 = 5

    3 x 2 + 1 = 7

    5 x 2 + 1 = 11

    7 x 2 + 1 = 15

    11 x 2 + 1 = 23

    13 x 2 + 1 = 27

    So,there are 4 jillyprimes which are less than 15 : 2 ; 3 ; 5 ; 11


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steve jobs
27/03/2017 at 11:05
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It is given abc is a square number, n2. Also, a + b +c = n + 2. The value of n is

Prime Numbers and Composite Numbers


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steve jobs
27/03/2017 at 10:56
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Find a square number in the form of aabb

Prime Numbers and Composite Numbers

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    Nguyen Trong Quang 05/09/2019 at 15:40

    We have \(\overline{aabb}=11\times\overline{a0b}=11\times\left(100a+b\right)\)   

    11 divide by 4 give we remainder 3. A square number divide by 4 give me remainder 0 or 1 

    ==> Look in 100a + b . \(100a⋮4\) so if b : 4 give we re. 1 or 2 the 11(100a + b ) gives re. 3 or 2 (no!)

    So b : 4 must gives re. 3 or 4 , b is a digit ==> b = { 3 ; 4 ; 7 ; 8}. Square never have last dg. is 3;7 and 8 , so b =4

    With sentences above we get 100a + b (100a + 4) divide by 3 gives re. 2 or 0. Remember b = 4 = 3 + 1, so a : 3 gives re. 1or 2. Grouping a we get a = {1 ; 2 ; 4; 5; 7; 8}. Try each a you'll find a=7

    That number is 7744. A sq. of 88


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steve jobs
27/03/2017 at 10:56
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A palindrome is a number that reads the same forward and backward, 1234 and 4321, therefore, is called a palindromic pair.

Find a palindromic pair whose product is 101556

Prime Numbers and Composite Numbers


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steve jobs
27/03/2017 at 10:54
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a, b and c are all primes. The sum of their inverses is \(\dfrac{167}{385}\).Find the three primes

Prime Numbers and Composite Numbers


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steve jobs
27/03/2017 at 10:53
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The sum of three prime numbers is 96. Find the possible values of these primes

Prime Numbers and Composite Numbers


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steve jobs
27/03/2017 at 10:52
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It is given that abc is a prime number . Find the number of divisors for abcabc

Prime Numbers and Composite Numbers

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    »ﻲ2004#ﻲ« 29/03/2017 at 06:10

    We have : abcabc = abc x 1001 = abc x 7 x 11 x 13

    Because abc is a prime number,the number of divisors of abcabc is :

    (1 + 1)4 = 16

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    Number One 02/04/2017 at 06:29
    We have : abcabc = abc x 1001 = abc x 7 x 11 x 13

    Because abc is a prime number,the number of divisors of abcabc is :

    (1 + 1)4 = 16

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    Phạm Tuấn Kiệt 18/05/2017 at 19:49

    We have : abcabc = abc x 1001 = abc x 7 x 11 x 13

    Because abc is a prime number,the number of divisors of abcabc is :

    (1 + 1)4 = 16


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steve jobs
27/03/2017 at 10:51
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Roy is one year older than Sam. Sam is two years older than Tim. The product of their age is 3210 . How old is Tim?

Prime Numbers and Composite Numbers

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    Nguyễn Nhật Minh 01/06/2017 at 12:23

    Your problem is not true, because 3210 = 2 x 3 x 5 x 107, and noone in this problem can be 107 years old!


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Bill gates
20/03/2017 at 10:51
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Two numbers are relatively prime if their only common factor is 1. How mayny numbers less than 50 are relatively prime to 50 ?

Prime Numbers and Composite Numbers


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Bill gates
20/03/2017 at 10:49
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How many factors does the number 300 have?

Prime Numbers and Composite Numbers

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    Run my EDM 20/03/2017 at 12:40

    \(300=2^2.3.5^2\)

    The number of integer factors 300 have is \(2.\left[\left(2+1\right)\left(1+1\right)\left(2+1\right)\right]=36\)

    Ans : 36.

    Selected by MathYouLike
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    →இے๖ۣۜQuỳnh 22/03/2017 at 20:18

    You have : 300 = 22.3.52

    The number of integer factors 300 have is :

                          2.[(2 + 1)(1 + 1)(2 + 1)] = 36

                                   Answer : 36. good

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    »ﻲ†hïếu๖ۣۜGïลﻲ« 25/03/2017 at 18:59

    We have : 300 = 22.3.52

    The number of integer factors 300 have is :

                          2.[(2 + 1)(1 + 1)(2 + 1)] = 36

                                   Answer : 36. good


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Bill gates
20/03/2017 at 10:49
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How many ways are there to write 37 as the sum of at least three prime numbers ?

Prime Numbers and Composite Numbers

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    ¤« 24/02/2018 at 13:57

    We have : 37 = 3 + 5 + 29 (c1)

                     37 = 3 + 11 + 23 (c2)

                     37 = 5 + 13 + 19 (c3)

    Drees is three ways are there to write 37

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    Lê Nho Khoa 23/03/2017 at 21:07

    We have : 37 = 3 + 5 + 29 (c1)

                     37 = 3 + 11 + 23 (c2)

                     37 = 5 + 13 + 19 (c3)

    Drees is three ways are there to write 37 

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    Nguyễn Việt Hoàng 21/03/2017 at 06:12

    We have : 37 = 3 + 5 + 29 (c1)

                     37 = 3 + 11 + 23 (c2)

                     37 = 5 + 13 + 19 (c3)

    Drees is three ways are there to write 37 


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Bill gates
20/03/2017 at 10:48
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It is given 7m +n = mn +11 = prime, where m and n are both prime too.

Find \(m^2+n^2\).

Prime Numbers and Composite Numbers

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    ¤« 24/02/2018 at 13:57

    We have : 7m + n = mn + 11

    => 7m + n - mn = 11

    => m(7 - n) - 7 + n = 4

    => (m - 1)(7 - n) = 4

    So we have a table as shown :

    m - 1 1 2 4
    7 - n 4 2 1
    m 2 3 5
    n 3 5 6 (absurd)
    7m + n 17 26 (absurd) x

    Hence,we have m = 2 ; n = 3 and m2 + n2 = 13

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    Phan Thanh Tinh Coordinator 28/03/2017 at 19:51

    We have : 7m + n = mn + 11

    => 7m + n - mn = 11

    => m(7 - n) - 7 + n = 4

    => (m - 1)(7 - n) = 4

    So we have a table as shown :

    m - 1 1 2 4
    7 - n 4 2 1
    m 2 3 5
    n 3 5 6 (absurd)
    7m + n 17 26 (absurd) x

    Hence,we have m = 2 ; n = 3 and m2 + n2 = 13

     


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Bill gates
20/03/2017 at 10:46
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Determine if the follwing numbers are prime:

(a) 1997

(b) 123456789

(c) (23456719)

Prime Numbers and Composite Numbers

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    ¤« 24/02/2018 at 13:57

    Only 1997 is a prime number

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    Phan Thanh Tinh Coordinator 23/03/2017 at 17:34

    Only 1997 is a prime number


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