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Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2016 Junior Balkan Team Selection Tests - Moldova
1
Moldova Junior TST for JBMO 2016 - Problem 1
Moldova Junior TST for JBMO 2016 - Problem 1
Source:
February 29, 2016
number theory
Problem Statement
a
3
b
3
\frac{a^3}{b^3}
b
3
a
3
+
a
3
+
1
b
3
+
1
\frac{a^3+1}{b^3+1}
b
3
+
1
a
3
+
1
+...+
a
3
+
2015
b
3
+
2015
\frac{a^3+2015}{b^3+2015}
b
3
+
2015
a
3
+
2015
=2016 b - positive integer, b can't be 0 a - real Find
a
3
b
3
\frac{a^3}{b^3}
b
3
a
3
*
a
3
+
1
b
3
+
1
\frac{a^3+1}{b^3+1}
b
3
+
1
a
3
+
1
*...*
a
3
+
2015
b
3
+
2015
\frac{a^3+2015}{b^3+2015}
b
3
+
2015
a
3
+
2015
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