Consider this series: 1, 2, 3,..., N-1, N, N+1,..., M. Given 1 + 2 + 3 + ... + (N-1) = (N+1) + (N+2) +...+ M. Find N. (hint: N is a 4 digits number)
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Originally Posted by john_n82 Consider this series: 1, 2, 3,..., N-1, N, N+1,..., M. Given 1 + 2 + 3 + ... + (N-1) = (N+1) + (N+2) +...+ M. Find N. (hint: N is a 4 digits number) Note, Therefore, , therefore . We need the discriminant to be a square, so we need . This is a Pellian equation.
Last edited by ThePerfectHacker; March 7th 2009 at 02:08 PM.
Originally Posted by ThePerfectHacker Note, Therefore, , therefore . We need the discriminant to be a square, so we need . This is a Pellian equation. I found M = 8, so N = 6.
Originally Posted by john_n82 Consider this series: 1, 2, 3,..., N-1, N, N+1,..., M. Given 1 + 2 + 3 + ... + (N-1) = (N+1) + (N+2) +...+ M. Find N. (hint: N is a 4 digits number) i think you mean N^2 is a four-digit number in this case M = 49, N = 35
i found 2 more values for M M = 288, N = 204 M 9800, N = 6930 What is the exact answer for this problem?
Originally Posted by john_n82 i found 2 more values for M M = 288, N = 204 M 9800, N = 6930 What is the exact answer for this problem? There are many answers to this problem. You are told that you need N to be a 4 digit number so N=6930
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