I Can't....Can Anybody else?

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 $2^{n}+3=11^{k}$ .

#NumberTheory

Easy Math Editor

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`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Souryajit Roy If you can't, no one can ;)

Mehul Arora - 5 years, 8 months ago

Sweet Sarcasm

Souryajit Roy - 5 years, 7 months ago

Hey @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 - 5 years, 8 months ago

When you will give the solution ? It has been a month -_-

Souryajit Roy - 5 years, 6 months ago

Ohhh Sorry!! I forgot about this. I will provide you today.

Surya Prakash - 5 years, 6 months ago

@Surya Prakash – Finally I solved it...no longer in need of a solution

Souryajit Roy - 5 years, 6 months ago

@Souryajit Roy – Can you post the solution here? Plss

Surya Prakash - 5 years, 6 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 :(

Surya Prakash - 5 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$