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National and Regional Contests
Czech Republic Contests
Czech and Slovak Olympiad III A
2020 Czech and Slovak Olympiad III A
4
4
Part of
2020 Czech and Slovak Olympiad III A
Problems
(1)
b is perfect square when b^2 = a^2 + ab + b
Source: 2020 Czech and Slovak Olympiad III A p4
11/24/2020
Positive integers
a
,
b
a, b
a
,
b
satisfy equality
b
2
=
a
2
+
a
b
+
b
b^2 = a^2 + ab + b
b
2
=
a
2
+
ab
+
b
. Prove that
b
b
b
is a square of a positive integer. (Patrik Bak)
number theory
Perfect Square