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Finding three nonnegative integers...

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October 13, 2010
number theory unsolvednumber theory

Problem Statement

Let a,b,ca, b, c be nonnegative integers such that a≤b≤c,2b≠a+ca \le b \le c, 2b \neq a + c and a+b+c3\frac{a+b+c}{3} is an integer. Is it possible to find three nonnegative integers d,ed, e, and ff such that d≤e≤f,f≠cd \le e \le f, f \neq c, and such that a2+b2+c2=d2+e2+f2a^2+b^2+c^2 = d^2 + e^2 + f^2?
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