Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Prove it Soviet Union

Problem:

Which is greater: $31^{11}$ or $17^{14}$ ? [No calculators allowed!]

Solution

Solution:

$17^{2} = 289 > 9 \cdot 31$ . So $17^{14} > 9^{7} 31^{7}$ . But $3^{7} = 2187 > 31^{2}$ . Hence $17^{14} > 31^{11}$ .

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