I have two problems-

1.Find all primes \(p\) such that there are positive integers \(a\) and \(b\) for which \(p=a^{2}+b^{2}\) and \(a^{2}+b^{2}\) divides \(a^{3}+b^{3}-4\).

2.Find all natural numbers \(n\) and \(k\) such that \(2^{n}+3=11^{k}\).

I have two problems-

1.Find all primes \(p\) such that there are positive integers \(a\) and \(b\) for which \(p=a^{2}+b^{2}\) and \(a^{2}+b^{2}\) divides \(a^{3}+b^{3}-4\).

2.Find all natural numbers \(n\) and \(k\) such that \(2^{n}+3=11^{k}\).

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TopNewestHey @Souryajit Roy , I got the answer for problem 2. The only solution is \((3,1)\). I will post the solution soon. It's very easy. – Surya Prakash · 1 year, 5 months ago

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– Surya Prakash · 1 year, 3 months ago

Sorry, I lost the paper on which I wrote the solution. And I forgot the way I proved it as it is too long. Sorry :(Log in to reply

– Souryajit Roy · 1 year, 3 months ago

When you will give the solution ? It has been a month -_-Log in to reply

– Surya Prakash · 1 year, 3 months ago

Ohhh Sorry!! I forgot about this. I will provide you today.Log in to reply

– Souryajit Roy · 1 year, 3 months ago

Finally I solved it...no longer in need of a solutionLog in to reply

– Surya Prakash · 1 year, 3 months ago

Can you post the solution here? PlssLog in to reply

@Souryajit Roy If you can't, no one can ;) – Mehul Arora · 1 year, 5 months ago

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– Souryajit Roy · 1 year, 4 months ago

Sweet SarcasmLog in to reply