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Albert1
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given equation: $(n-1)x^2-px+n=0 $ has two positive integer solutions , (here $n,p \in N$)
prove :$p^p-n^n=23$
prove :$p^p-n^n=23$
Albert said:given equation: $(n-1)x^2-px+n=0 $ has two positive integer solutions , (here $n,p \in N$)
prove :$p^p-n^n=23$
The equation p^p-n^n=23 is used to test the validity of the Goldbach's conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers.
To prove p^p-n^n=23, you would need to find a combination of two prime numbers, p and n, that when raised to the power of themselves and subtracted, result in the value of 23. This would serve as a counterexample to the Goldbach's conjecture, proving it to be false.
The possible solutions for p and n in the equation p^p-n^n=23 are dependent on the value of 23. If 23 is a prime number, then p and n would both have to be 2. If 23 is not a prime number, then there could be multiple solutions for p and n. For example, if 23 is expressed as 5+18, then p could be 2 and n could be 3 or 17.
Yes, the equation p^p-n^n=23 can be solved using a computer program. In fact, in 2014, a group of mathematicians used a computer program to find a counterexample for the Goldbach's conjecture, disproving it for a certain range of numbers. However, the equation can also be solved manually by trying out different combinations of prime numbers.
No, as of now, the equation p^p-n^n=23 has not been solved. The Goldbach's conjecture remains an unsolved problem in mathematics, and there is no known solution for the equation. However, there have been attempts to find a counterexample, and the search is still ongoing.