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 3 Simultaneous Diophantine approximation: multiple solutions required 2 Is there a “positive” definition for irrational numbers? 2 show that $\{ nq^{\frac{1}{3}} \} + \{ nq^{\frac{2}{3}} \} \geq Cn^{-\frac{1}{2}}$ 2 Simultaneous Diophantine approximation in the non-generic case 2 How to avoid getting bogged down in details in proofs?

### Reputation (562)

 +25 Units in Cube Root System +10 Simultaneous Diophantine approximation: multiple solutions required +10 Does there exist a prime that is only consecutive digits starting from 1? +10 Is there a “positive” definition for irrational numbers?

### Questions (9)

 9 What is the period of this sequence? 5 Can a large number of small matrices be multiplied quickly? 4 How to find the area of these sets? 2 Prime numbers like 113 1 How to find this Littlewood conjecture estimate?

### Tags (26)

 9 number-theory × 9 3 irrational-numbers × 2 8 diophantine-approximation × 7 2 soft-question × 4 5 ergodic-theory × 2 2 algebra-precalculus × 2 4 prime-numbers × 5 2 gcd-and-lcm 3 elementary-number-theory × 6 2 diophantine-equations

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