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National and Regional Contests
Turkey Contests
JBMO TST - Turkey
2022 JBMO TST - Turkey
1
1
Part of
2022 JBMO TST - Turkey
Problems
(1)
(a^2+b^2)/(a-b)^2 is an integer => (a^3+b^3)/(a-b)^3 is an integer
Source: 2022 Turkey JBMO TST P1
3/15/2022
For positive integers
a
a
a
and
b
b
b
, if the expression
a
2
+
b
2
(
a
−
b
)
2
\frac{a^2+b^2}{(a-b)^2}
(
a
−
b
)
2
a
2
+
b
2
is an integer, prove that the expression
a
3
+
b
3
(
a
−
b
)
3
\frac{a^3+b^3}{(a-b)^3}
(
a
−
b
)
3
a
3
+
b
3
is an integer as well.
number theory
Integers
Divisibility