Diophantine equations of Erdös-Moser type
1996 ◽
Vol 53
(2)
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pp. 281-292
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Keyword(s):
Using an old result of Von Staudt on sums of consecutive integer powers, we shall show by an elementary method that the Diophantine equation 1k + 2k + … + (x − l)k = axk has no solutions (a, x, k) with k > 1, . For a = 1 this equation reduces to the Erdös-Moser equation and the result to a result of Moser. Our method can also be used to deal with variants of the equation of the title, and two examples will be given. For one of them there are no integer solutions with
2018 ◽
Vol 36
(3)
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pp. 173-192
2013 ◽
Vol 753-755
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pp. 3149-3152
2018 ◽
2015 ◽
Vol 729
◽
pp. 220-223
Keyword(s):
2018 ◽
2021 ◽
Vol 27
(3)
◽
pp. 113-118
2006 ◽
Vol 02
(02)
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pp. 195-206
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Keyword(s):
2014 ◽
Vol 687-691
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pp. 1182-1185