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Iran MO (2nd Round)
2019 Iran MO (2nd Round)
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Number theory , Iran MO 2019
Number theory , Iran MO 2019
Source: Iran MO 2019, secound round, day 1, p3
May 2, 2019
number theory
Problem Statement
x
1
,
x
2
,
.
.
.
,
x
n
>
1
x_1,x_2,...,x_n>1
x
1
,
x
2
,
...
,
x
n
>
1
are natural numbers and
n
≥
3
n \geq 3
n
≥
3
Prove that :
(
x
1
x
2
.
.
.
x
n
)
2
≠
x
1
3
+
x
2
3
+
.
.
.
+
x
n
3
(x_1x_2...x_n)^2 \ne x_1^3 + x_2^3 +...+x_n^3
(
x
1
x
2
...
x
n
)
2
=
x
1
3
+
x
2
3
+
...
+
x
n
3
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