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Latvia BW TST
2021 Latvia Baltic Way TST
P14
P14
Part of
2021 Latvia Baltic Way TST
Problems
(1)
Infinitely many solutions to floor equation
Source: Latvia BW TST 2021 P14
9/26/2021
Prove that there exist infinitely many triples of positive integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
so that
a
,
b
,
c
a,b,c
a
,
b
,
c
are pairwise coprime and
⌊
a
2
2021
⌋
+
⌊
b
2
2021
⌋
=
⌊
c
2
2021
⌋
.
\bigg \lfloor \frac{a^2}{2021} \bigg \rfloor + \bigg \lfloor \frac{b^2}{2021} \bigg \rfloor = \bigg \lfloor \frac{c^2}{2021} \bigg \rfloor.
⌊
2021
a
2
⌋
+
⌊
2021
b
2
⌋
=
⌊
2021
c
2
⌋
.
number theory
floor function