AO1992

 9 How to proceed with following determinant inequality 7 Minimum of $x^2+y^2+z^2-2xyz$ 6 Prove that for every $n\geq6$ the equation $1/a_1^2 + … 1/a_n^2 = 1$ has answer in $\mathbb{Z}$ 5 Find all $(x,y)$ of positive integers s.t. $x^3-y^3=xy+61$ 4 Can I not use QM-AM inequality to solve this?

Reputation (1,328)

 +25 Does the sequence $x_n = \sin\left([\text{first } n \text{ digits of } \pi] \cdot 10^{n - 1} \right)$ converge? +40 Can I not use QM-AM inequality to solve this? +65 Find all $(x,y)$ of positive integers s.t. $x^3-y^3=xy+61$ +15 Prove that $a + b + c + 2 >= abc$

Tags (60)

 26 inequality × 11 10 determinant × 2 19 number-theory × 5 9 calculus × 2 17 linear-algebra × 4 7 combinatorics × 2 10 real-analysis × 9 7 multivariable-calculus 10 induction × 3 6 sequences-and-series × 4

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