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A082176
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Professor E.P.B. Umbugio's sequence.
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2
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0, 0, 206276, 1124101062, 4106026092896, 12565214785548390, 34787981278581970376, 90353184628933414448862, 224610989213093282203310816, 541037084832262355204120965110
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OFFSET
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0,3
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COMMENTS
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The problem was to prove that 1946 divides every a(n). The proof uses 2141-1770 = 371 = 1863-1492 and 2141-1863= 278 = 1770-1492, gcd(278,371)=1, 278*371=53*1946 and the fact that x-y not 0 divides x^n-y^n for n>=0. See the Starke reference. The primes which divide every a(n) are 2,7,53,139. Note the historical dates other than 2141 in the formula. This AMM problem was proposed in 1946 (with a reference to April 1).
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REFERENCES
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H. E. G. P., Elementary problem No. E716, Professor Umbugio's Prediction; Solution by E. P. Starke, American Math. Monthly 54 (1947) 43-4.
C. A. Pickover, Die Mathematik und das Goettliche, Spektrum Akademischer Verlag, Heidelberg, Berlin, 1999, pp. 56-8,398 (English: The Loom of God, Plenum, 1997).
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LINKS
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Table of n, a(n) for n=0..9.
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FORMULA
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a(n)= 1492^n - 1770^n - 1863^n + 2141^n.
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CROSSREFS
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Cf. A082177, A082178.
Sequence in context: A206093 A177006 A115946 * A178285 A101701 A092011
Adjacent sequences: A082173 A082174 A082175 * A082177 A082178 A082179
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Apr 25 2003
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STATUS
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approved
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