Algebra · Integer squares · Extremal problems · Cyclic conditions
Problem 1, 2026
← Prev · 1 / 69 · Next →Let \(a\), \(b\), \(c\), \(d\) and \(e\) be integers such that
\[ a \ne b, \qquad b \ne c, \qquad c \ne d, \qquad d \ne e, \qquad e \ne a. \]
Determine the smallest possible value of the expression
\[ I = a^{2} + b^{2} + c^{2} + d^{2} + e^{2}. \]
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Serbian Municipal Competition 2026, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source