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Found problems: 1

2004 Alexandru Myller, 1
Tags: cyclic equality , number theory , algebra
Let be a nonnegative integer $ n $ and three real numbers $ a,b,c $ satisfying $$ a^n+c=b^n+a=c^n+b=a+b+c. $$ Show that $ a=b=c. $ [i]Gheorghe Iurea[/i]