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| Another 2009 Problem (Posted on 2006-12-26) |
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Determine analytically if x3+y4=2009 has any solution in integers.
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Submitted by K Sengupta
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Rating: 4.0000 (1 votes)
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Solution:
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At the outset, we observe that 2009 = 7 (Mod 13)
The cubic residues in modulo 13 system are (0,1,5,8,12) while the quartic residues in the modulo 13 system are (0,1,3,9).
Considering exacly one element out of (0,1,5,8,12) and exactly one element out of (0,1,3,9) and adding the two integers, we obtain 20 sums, none of which possesses the form 7 ( Mod 13).
Consequently, no integer solution is possible for the given problem.
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Date |
 | Two answers | Old Original Oskar! | 2006-12-26 11:13:23 |
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