HMMT 2024 U7

Guts
Answer

Positive integers $a, b$ , and $c$ have the property that $a^{b}, b^{c}$ , and $c^{a}$ end in 4,2 , and 9 , respectively. Compute the minimum possible value of $a+b+c$ .

Dataset text NuminaMath olympiads. Quoted with source.

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