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Let $a, b, c, d$ be fixed integers with $d$ not divisible by $5$. Assume that $m

Source: 1900 Eotvos p1

March 19, 2020
algebra

Problem Statement

Let a,b,c,da, b, c, d be fixed integers with dd not divisible by 55. Assume that mm is an integer for which am3+bm2+cm+dam3 +bm2 +cm+d is divisible by 55. Prove that there exists an integer nn for which dn3+cn2+bn+adn3 +cn2 +bn+a is also divisible by 55.
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