can a prime number be a prefect square ? justify your answer .
Answers
Answered by
0
a prime number never be a perfect square because the square number's root will be it factor. then how it is possible.
Answered by
0
Find all primes p and q such that p2+7pq+q2 is a perfect square.
One obvious solution is p=q and under such a situation all primes p and q will satisfy.
Further if p≠q then we can assume without the loss of generality that p>q. Assuming this and that there exists at least one such perfect square I have tried to show some contradiction modulo 4 as any odd perfect square leaves a remainder of 1 when divided by 4, but it is not working. However I firmly believe that p=q is the only solution, but I have failed to prove this.
One obvious solution is p=q and under such a situation all primes p and q will satisfy.
Further if p≠q then we can assume without the loss of generality that p>q. Assuming this and that there exists at least one such perfect square I have tried to show some contradiction modulo 4 as any odd perfect square leaves a remainder of 1 when divided by 4, but it is not working. However I firmly believe that p=q is the only solution, but I have failed to prove this.
Similar questions