Integer equation + prime numbers - practice problems
Number of problems found: 45
- Primes 2
For what primes p,q,r is true: p²-(q+r)²=647 - Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Diofant equation
250x + 120y = 5640 - One hundred stamps
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 stamp? How many does the problem have solutions? - How many
How many different rectangles with integer side lengths have an area S = 60 cm²? - Cherries
Cherries in the bowl can be divided equally among 20 or 15, or 10 children. How many are the minimum cherries in the bowl? - Rectangles
How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles. - Divisibility
Determine the smallest integer which divided 11 gives remainder 4. When divided, 15 gives remainder 10 and when divided by 19 gives remainder 16. - Diofant 2
Is equation 70x +52y = 34 solvable on the set of integers Z? - Chocolate
I have a box of chocolate - white, milk, and dark. The ratio of white to milk with dark is 3:4. The ratio of white and milk to dark is 17:4. Calculate the ratio between white, milk, and dark chocolate. - Several 8130
The hotel has 27 beds in several rooms. There are single, double and triple rooms. How many single, double and triple rooms can there be in the hotel? Give at least three options. - Rectangles 70304
How many rectangles with side lengths expressed in natural numbers have an area of 96 cm²? - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Seedcake
Seedcake costs 44 cents. How many minimum seedcakes must we buy that we can pay in cash, only whole euros? - Revolutions 24121
The white wheel has 24 teeth. The black wheel has fewer teeth than the white wheel. Both wheels return to their initial position for the first time after two revolutions of the white wheel. How many teeth does the black wheel have? - Parakeets 80471
Mr. Spacek keeps birds. It has more than 50 and less than 100. Parakeets make up a ninth and canaries a quarter of the total. How many birds did he keep? - Notebooks 8651
I need to buy exercise books and covers. One notebook costs CZK 12, and one cover costs CZK 3. I have one fifty crown and one twenty crown. How many notebooks and covers can I buy for it? Come up with more options. - Two-digit number
In a two-digit number, the number of tens is three greater than the number of units. If we multiply the original number by a number written in the same digits, but in reverse order, we get product 3 478. Find the original number. - Mushrooms from the forest
Magda and Tereza go to pick mushrooms. Found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms were found, Magda? - Diofant equation
In the set of integers (Z), solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
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