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Problems
Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan Junior National Olympiad
2022 Azerbaijan Junior National Olympiad
N2
N2
Part of
2022 Azerbaijan Junior National Olympiad
Problems
(1)
prove that 6|x,y,z
Source: Azerbaijan 2022 Junior National Olympiad
5/14/2022
If
x
,
y
,
z
∈
N
x,y,z \in\mathbb{N}
x
,
y
,
z
∈
N
and
2
x
2
+
3
y
3
=
4
z
4
2x^2+3y^3=4z^4
2
x
2
+
3
y
3
=
4
z
4
, Prove that
6
∣
x
,
y
,
z
6|x,y,z
6∣
x
,
y
,
z
number theory
modulo
Azerbaijan
Junior