Unknown number

Unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies:
• Difference first and second prime number is half the difference between the third and second prime numbers.
• The product of the difference the second with the first primes
and difference the third and the second prime number is a multiple of 17.

Determine the smallest number that has all the above properties.

Correct result:

n =  2014

Solution:

2014= 2 × 19 × 53
$primes = array(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67);
for($a=0;$a<count($primes); $a++)
{
    for($b=$a+1;$b<count($primes); $b++)
    {
        for($c=$b+1;$c<count($primes); $c++)
        {
            $p1 = $primes[$a];
            $p2 = $primes[$b];
            $p3 = $primes[$c];

            if($p2-$p1 == 0.5*($p3-$p2) &&  mod(($p2-$p1)*($p3-$p2),17)==0)
            {
                $rv[$p1*$p2*$p3] = "$p1 $p2 $p3";
            }

        }
    }

}
ksort($rv);
print_r($rv);




Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Divisors
    divisors The sum of all divisors unknown odd number is 2112. Determine sum of all divisors of number which is twice of unknown numbers.
  • Combinations
    circles How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
  • Amazing number
    numbers4 An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.
  • Numbers
    primes Write smallest three-digit number, which in division 5 and 7 gives the rest 2.
  • Chebyshev formula
    ChebyshevSpiral To estimate the number of primes less than x is used Chebyshev formula: ? Estimate the number of primes less than 30300537.
  • Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
  • Teams
    football_team How many ways can divide 16 players into two teams of 8 member?
  • Examination
    examination The class is 21 students. How many ways can choose two to examination?
  • PIN - codes
    pin How many five-digit PIN - code can we create using the even numbers?
  • Candies
    bonbons_2 In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?
  • Cards
    cards_2 Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probab
  • Repair company
    servis The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 8 residue cars. How many total cars company repaired?
  • Sequence 2
    seq2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  • Trigonometry
    sinus Is true equality? ?
  • Line
    skew_lines It is true that the lines that do not intersect are parallel?