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# Problems of the day

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Jatin Kr Dey
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Problem 1

For each positive integer  n   let $$x_n=p_1+…..+p_n$$ where $$p_{1},…..,p_{n}$$ are the first n primes. Prove that for each positive integer n, there is an integer $$k_{n}$$ such that $$x_{n}<k_n^2<x_{n+1}$$ .

Problem 2

Find, with justification, all positive real numbers   a, b, c satisfying the system of equations:    $$a\sqrt{b}=a+c,b\sqrt{c}=b+a,c\sqrt{a}=c+b$$

• This topic was modified 1 week, 2 days ago by  Jatin Kr Dey.
• This topic was modified 1 week, 2 days ago by  Jatin Kr Dey.
• This topic was modified 1 week, 2 days ago by  Jatin Kr Dey.
• This topic was modified 1 week, 2 days ago by  Jatin Kr Dey.
• This topic was modified 1 week, 2 days ago by  Jatin Kr Dey.
• This topic was modified 1 week, 2 days ago by  Jatin Kr Dey.
• This topic was modified 1 week, 2 days ago by  Jatin Kr Dey.
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