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2015a^2+a = 2016b^2+b, \sqrt{a-b} is natural (HOMC 2016 J Q14)
2015a^2+a = 2016b^2+b, \sqrt{a-b} is natural (HOMC 2016 J Q14)
Source:
August 6, 2019
algebra
radical
natural
Problem Statement
Given natural numbers
a
,
b
a,b
a
,
b
such that
2015
a
2
+
a
=
2016
b
2
+
b
2015a^2+a = 2016b^2+b
2015
a
2
+
a
=
2016
b
2
+
b
. Prove that
a
−
b
\sqrt{a-b}
a
−
b
is a natural number.
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