Difference between revisions of "2001 JBMO Problems/Problem 1"
(Completely FIXED the solution)
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Now <math>b^3 + c^3 = 1001.</math> Since <math>b^3 \ge c^3,</math> we find that <math>2b^3 \ge 1001.</math>
Now <math>b^3 + c^3 = 1001.</math> Since <math>b^3 \ge c^3,</math> we find that <math>2b^3 \ge 1001.</math> <math>b = 10</math> and <math>c = 1.</math>
Latest revision as of 21:48, 11 August 2018
Solve the equation in positive integers.
Note that for all positive integers the value is congruent to modulo Since we find that Thus, and the only numbers congruent to modulo are
WLOG, let That means and Thus, so
Now Since we find that That means and
In summary, the only solutions are
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