When is $u_n$ defined by $u_1=1,u_n=(n-1)u_{n-1}+1$ divisible by $n$?
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Problem statement : for which values of $n$ is $u_n$ defined by $u_1=1,u_n=(n-1)u_{n-1}+1$ divisible by $n$ ?
I have tried introducing an auxiliary recurrence relation like $v_n=u_n-1$ but this is not getting me anywhere.
I have also tried computing the first few values of $u_n$ but I cannot see a pattern.
Note : this is denoted as 'hard' in my text, 'The Mathematical Olympiad Handbook - an introduction to problem solving' by A.Gardiner.
elementary-number-theory recurrence-relations
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
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add a comment |
$begingroup$
Problem statement : for which values of $n$ is $u_n$ defined by $u_1=1,u_n=(n-1)u_{n-1}+1$ divisible by $n$ ?
I have tried introducing an auxiliary recurrence relation like $v_n=u_n-1$ but this is not getting me anywhere.
I have also tried computing the first few values of $u_n$ but I cannot see a pattern.
Note : this is denoted as 'hard' in my text, 'The Mathematical Olympiad Handbook - an introduction to problem solving' by A.Gardiner.
elementary-number-theory recurrence-relations
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
$endgroup$
add a comment |
$begingroup$
Problem statement : for which values of $n$ is $u_n$ defined by $u_1=1,u_n=(n-1)u_{n-1}+1$ divisible by $n$ ?
I have tried introducing an auxiliary recurrence relation like $v_n=u_n-1$ but this is not getting me anywhere.
I have also tried computing the first few values of $u_n$ but I cannot see a pattern.
Note : this is denoted as 'hard' in my text, 'The Mathematical Olympiad Handbook - an introduction to problem solving' by A.Gardiner.
elementary-number-theory recurrence-relations
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
$endgroup$
Problem statement : for which values of $n$ is $u_n$ defined by $u_1=1,u_n=(n-1)u_{n-1}+1$ divisible by $n$ ?
I have tried introducing an auxiliary recurrence relation like $v_n=u_n-1$ but this is not getting me anywhere.
I have also tried computing the first few values of $u_n$ but I cannot see a pattern.
Note : this is denoted as 'hard' in my text, 'The Mathematical Olympiad Handbook - an introduction to problem solving' by A.Gardiner.
elementary-number-theory recurrence-relations
elementary-number-theory recurrence-relations
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
edited Dec 21 '18 at 4:07
user3203476
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
asked Dec 21 '18 at 3:59
user3203476user3203476
746613
746613
add a comment |
add a comment |
1 Answer
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This is likely a problem that has never been corrected; see this post for your exact problem, and check out the comments.
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
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1 Answer
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1 Answer
1
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oldest
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$begingroup$
This is likely a problem that has never been corrected; see this post for your exact problem, and check out the comments.
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
$endgroup$
add a comment |
$begingroup$
This is likely a problem that has never been corrected; see this post for your exact problem, and check out the comments.
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
$endgroup$
add a comment |
$begingroup$
This is likely a problem that has never been corrected; see this post for your exact problem, and check out the comments.
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
$endgroup$
This is likely a problem that has never been corrected; see this post for your exact problem, and check out the comments.
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
answered Dec 21 '18 at 4:37
DanielJackDanielJack
661
661
add a comment |
add a comment |
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