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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