Given the prime numbers P and Q, the expressions 2p + 1q and 2q − 3P are natural numbers

Let P ≥ Q, then 1 ≤ 2q − 3P = 2 × qp-3p < 2, then only 2q − 3P = 1, that is, P = 2q-3, then 2p + 1q = 4q − 5q = 4-5q, if 2p + 1q is a natural number, only q = 5, then p = 7, then P < Q, then 1 ≤ 2p + 1q = 2 × PQ + 1q < 3, then there are two cases: 2p + 1q = 1, q = 2p + 1

Given that P and Q are prime numbers and 2p + 3Q = 24, what is the QP cube

No solution
p=12-3q/2
P is positive, so Q must be even
Q can only be 0,2,4,6,8
P is 12,9,6,3,0
Obviously, there is no valid solution

RELATED INFORMATIONS

1. p. If q is prime and 3Q ^ 2 + 5p = 517, then p + q =?
2. The coordinates of point P are (1, - 1), and point q is a point on the straight line x + y-4 = 0. When vector PQ is perpendicular to vector a = (1. - 1), module PQ|=
3. This is a mathematical problem, 3Q ~ (≥ ▽≤)/~ There are 400 pages in a book. The page numbers are 1, 2, 3, 4.398 and 399. How many numbers are there in the number of pages?
4. When p is a prime number, 17p + 1 is a square number
5. The sum of two prime numbers is 13. Find the product of this number
6. Goldbach conjecture is verified in VB. All even numbers between 6 and 100 are required to be expressed as the sum of two prime numbers. The results are displayed in the list box, and the number of pairs is displayed Required output 6 = 3 + 3 8=3+5 10=3+7 10=5+5 Note that for example, 10, can be split into several pairs to show
7. A VB topic, verify "Goldbach conjecture: any even number greater than 6, can be expressed as the sum of two primes", from the keyboard input a greater than 6 Verify "Goldbach conjecture: any even number greater than 6 can be expressed as the sum of two prime numbers", input an even number greater than 6 from the keyboard, and print out all decomposition results_ Click() n = Val (InputBox ("input an even number greater than 6")) if n
8. Any prime plus odd is even
9. Write the odd, even, prime, and number from 20 to 40
10. In natural numbers 20 ~ 30, even numbers have (); odd numbers have (); prime numbers have (); and sum numbers have ()
11. P is prime, the sixth power of P + 3 is prime, and the 11th power of P - 52 = ()
12. The sum of two prime numbers is 999. Write these two prime numbers
13. The number of odd and composite numbers in one digit, the number of even and prime numbers in ten digit is two digit______ ．
14. A certain number is a four digit number divisible by 2 and 3, the number on the thousand digit is odd and composite, the number on the hundred digit is neither prime nor composite, and the number on the ten digit is the smallest composite, so the four digit number is a number______ ．
15. A three digit number is neither a prime nor a composite number on the hundreds, but the largest odd number on the tens, and the number is a multiple of 2 and 3. The three digit number is______ Or______ ．
16. The thousand bits of a number are the smallest odd numbers, the ten thousand bits are the smallest composite numbers, the ten bits are the smallest prime numbers, and the other digits are zeros______ It's both______ It's a multiple of______ A multiple of
17. The sum of not even numbers within 10 is______ The prime number that is not odd is______ ．
18. There are two prime numbers, the sum of which is an odd number less than 100 and a multiple of 17. Find these two prime numbers
19. I and the other number are prime numbers. Our sum is 19. Who are these two numbers?
20. If a four digit number is the product of three primes and the sum of the squares of the three primes is 39630, then the natural number is?