Square + prime numbers - practice problems
Number of problems found: 48
- Primes 2
For what primes p,q,r is true: p²-(q+r)²=647 - Two-digit 4750
My number for today: the product of the square of the smallest prime number with the smallest two-digit prime number - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Rectangles
How many rectangles with area 3152 cm² whose sides are natural numbers? - Probability 17013
What is the probability that a randomly written two-digit number from number 20 to number 99 will be divisible by 11, the power of number 3, or a prime number? - Square room
What is the size of the smallest square room, which can be paved with tiles with dimensions of 55 cm and 45 cm? How many such tiles are needed? - Determine 79374
Determine how many pieces of squares the chocolate would have if, after dividing it into the smallest pieces of the square, we would divide it without remainder between five and three people equally to each person. - Tiles
How many tiles of 20 cm and 30 cm can build a square if we have a maximum of 100 tiles? - Trams 2
Square passes two lines of the tram. One is running every nine minutes, the second interval of 15 minutes. Exactly at noon arrived two tram lines in the square. How soon should a similar situation arise again? - Rectangular 82582
We have to pave the smallest possible square with rectangular tiles with 168 cm and 280 cm sides. What will its side of the square be? - Expression 4451
Find the largest natural number d that has that property for any natural number the number n is the value of the expression V (n) = n ^ 4 + 11n²−12 is divisible by d. - Maximally 4036
Mr. Novák wants to pave the terrace with tiles of two sizes to be as small as possible. Its terrace is square with a side 3 meters long. There is a wall of the house on two sides of the terrace. Next to the wall, he wants to put small tiles, the rest larg - Tiles
From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 275 tiles. - Three 205
Three metallic bars of lengths 400 cm, 600 cm, and 720 cm are cut into equal pieces. Find the largest possible area of a square that can be made from any of the three bars. - Glass panel
A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut? - Infinitely 3818
We have 2 numbers. If we multiplied the first number's third root by the second number's square root, we would get the number 18. Determine these 2 numbers. Calculate only the integer solution if the problem has infinitely many solutions in the set of rea - The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets and their products was the power of the prime number. Find all possible ticket prices. - Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around the 3rd century A. D. Thanks to an admirer of his, who described his life through an algebraic riddle, we know at least something about his life. Diophantus's youth - Two gears
The gearbox will use a large gear to turn a smaller gear. The large gear will make 75 revolutions per minute, while the smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM - Two rectangles
I cut out two rectangles with 54 cm² and 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together, I get a rectangle with an area of 144 cm². What dimensions can this large rectangle have? Write all options. Explain your
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