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Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2013 Saudi Arabia Pre-TST
3.2
3.2
Part of
2013 Saudi Arabia Pre-TST
Problems
(1)
if 19 divides a_1^9+a_2^9+...+a_9^9 then also divides a_1a_2...a_9
Source: 2013 Saudi Arabia Pre-TST 3.2
9/13/2020
Let
a
1
,
a
2
,
.
.
.
,
a
9
a_1, a_2,..., a_9
a
1
,
a
2
,
...
,
a
9
be integers. Prove that if
19
19
19
divides
a
1
9
+
a
2
9
+
.
.
.
+
a
9
9
a_1^9+a_2^9+...+a_9^9
a
1
9
+
a
2
9
+
...
+
a
9
9
then
19
19
19
divides the product
a
1
a
2
.
.
.
a
9
a_1a_2...a_9
a
1
a
2
...
a
9
.
number theory
divides
divisible