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Part of 2011 Irish Math Olympiad

Problems(2)

System of 6 Equations

Source: 2011 IrMO Paper 1 Problem 1

abc\neq 0

. Express in terms of

a,b,

c

x,y,z,u,v,w

of the equations x+y=a, z+u=b, v+w=c, ay=bz, ub=cv, wc=ax.

Sum is not an Integer

Source: 2011 IrMO Paper 2 Problem 1

\frac{2}{3}+\frac{4}{5}+\dots +\frac{2010}{2011}

is not an integer.