MathDB

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Part of 2010 Spain Mathematical Olympiad

Problems(2)

'pucelana' sequence of 16 consecutive odd integers

Source: Spain MO 2010

2/11/2011
A pucelana sequence is an increasing sequence of 1616 consecutive odd numbers whose sum is a perfect cube. How many pucelana sequences are there with 33-digit numbers only?
number theory proposednumber theory
Spain MO 4 - Inequality

Source: Spain MO 2010

8/16/2010
Let a,b,ca,b,c be three positive real numbers. Show that a+b+3c3a+3b+2c+a+3b+c3a+2b+3c+3a+b+c2a+3b+3c≥158 \frac {a+b+3c}{3a+3b+2c}+\frac {a+3b+c}{3a+2b+3c}+\frac {3a+b+c}{2a+3b+3c} \ge \frac {15}{8}
inequalitiesthree variable inequality