If $a,b\in \mathbb {N}_0$, show that $\sqrt {a}+\sqrt {b}$ is rational iff both of $a$ and $b$ are
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Phlembac Adib Hasan wrote: Problem 4: (Posted before)
If $a,b\in \mathbb {N}_0$, show that $\sqrt {a}+\sqrt {b}$ is rational iff both of $a$ and $b$ are integers.
Source: Self-made.
Sorry, for the typo. Edited now.Fahim Shahriar wrote:Phlembac Adib Hasan wrote: Problem 4: (Posted before)
If $a,b\in \mathbb {N}_0$, show that $\sqrt {a}+\sqrt {b}$ is rational iff both of $a$ and $b$ are integers.
Source: Self-made.
Is it true ?
assume the numbers are $a,b,c$Fahim Shahriar wrote:Problem 5:
The sum of three numbers is $6$, the sum of their squares is $8$, and the sum of their cubes is $5$. What is the sum of their fourth powers?
Source: অলিম্পিয়াড সমগ্র বই
So $a^4+b^4+c^4=0$
Phlembac Adib Hasan wrote:Let me know whether I am right.
Sophie Jermain kills it.Phlembac Adib Hasan wrote:Problem 6: Find all integers $n$ such that $n^4+4$ is a prime.
Source: http://www.brilliantscholars.com/assess ... ry/114744/
i couldn't get that ..... i did problem 6 with factorising which results $1,-1$. i think this is general way.Tahmid Hasan wrote: Sophie Jermain kills it.