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Moldova Contests
JBMO TST - Moldova
2020 Junior Balkan Team Selection Tests - Moldova
8
8
Part of
2020 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
JBMO TST Moldova Problem 8
Source:
10/14/2020
Find the pairs of real numbers
(
a
,
b
)
(a,b)
(
a
,
b
)
such that the biggest of the numbers
x
=
b
2
−
a
−
1
2
x=b^2-\frac{a-1}{2}
x
=
b
2
−
2
a
−
1
and
y
=
a
2
+
b
+
1
2
y=a^2+\frac{b+1}{2}
y
=
a
2
+
2
b
+
1
is less than or equal to
7
16
\frac{7}{16}
16
7
number theory