Diofant 2

Is equation
70x+52y=3470x +52y = 34
solvable on the set of integers Z?

Result




Solution:

70=2⋅5⋅752=22⋅13GCD(70,52)=2=2  342=17∈Z70 = 2 \cdot 5 \cdot 7 \\ 52 = 2^2 \cdot 13 \\ \text{GCD}(70, 52) = 2 = 2\\ \ \\ \ \\ \dfrac{ 34 }{ 2 } = 17 \in Z

The equation is a linear Diofant equation with positive coefficients

The equation has 0 positive integer solutions


Calculated by our Diofant problems and integer equations.

Try another example






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




Following knowledge from mathematics are needed to solve this word math problem:

Do you want to calculate greatest common divisor two or more numbers? Do you solve Diofant problems and looking for a calculator of Diofant integer equations?

Next similar math problems:

  1. Diofant equation
    diofantos In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
  2. Legs
    zidle In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
  3. One hundred stamps
    stamp_4 A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths , one crown, two-crown and five-crown. How many are each type of stamps? How many does the problem have solutions?
  4. Red and white
    tulipany Simona picked 63 tulips in the garden and tied bicolor bouquets for her girlfriends. The tulips were only red and white. She put as many tulips in each bouquet, three of which were always red. How much could Simon tear off white tulips? Write all the optio
  5. Two unknown numbers
    numbers_49 One number is 2 less than a second number. Twice the second number is 14 less than 5 times the first. Find the two numbers.
  6. Balls
    kulicky Michal said to Martin: give me one ball and I'll have twice as you. Martin said: give me 4 and we will have equally. How many balls each have?
  7. Gauss
    kfgauss Help little C.F. Gauss sum all the integers from 1 to 400.
  8. Sum of two primes
    prime_1 Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
  9. Tissues
    harmasan The store got three kinds of tissues - 132 children, 156 women and 204 men. Tissues each species were packed into boxes after the number of pieces the same for all three types (and greatest). Determine the number, if you know that every box has more than 6
  10. Toy cars
    numbers2_13 Pavel has a collection of toy cars. He wanted to regroup them. But in the division of three, four, six, and eight, he was always one left. Only when he formed groups of seven, he divided everyone. How many toy cars have in the collection?
  11. Numbers
    primes Write smallest three-digit number, which in division 5 and 7 gives the rest 2.
  12. 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.
  13. Seamstress 2
    krajcirka_1 Seamstress bought two kinds of textile in whole meters. One at 50 SKK and the second 70 SKK per meter. How many meter bought from this two textiles when paid totally 1540 SKK?
  14. Bundle of candies
    bonbons_3 In the store has 168 chocolates, caramel candies 224 and 196 hard candies. How many packages we can do and how many of candies will be in each package?
  15. 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.
  16. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  17. Basket of fruit
    hrusky_jablka In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which