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Dutch Mathematical Olympiad
1969 Dutch Mathematical Olympiad
1
1
Part of
1969 Dutch Mathematical Olympiad
Problems
(1)
min n, such that n = (a - 1) mod $a$ for all a \in {2,3,..., 10 }
Source: Netherlands - Dutch NMO 1969 p1
1/31/2023
Determine the smallest
n
n
n
such that
n
≡
(
a
−
1
)
n \equiv (a - 1)
n
≡
(
a
−
1
)
mod
a
a
a
for all
a
∈
{
2
,
3
,
.
.
.
,
10
}
a \in \{2,3,..., 10\}
a
∈
{
2
,
3
,
...
,
10
}
.
number theory
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