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 Choose To Prime Poser (Posted on 2010-04-18)
Determine all possible values of a positive integer N ≥ 3, such that NC2 – 1 is a prime power.

Note: NC2 represents N choose 2.

 See The Solution Submitted by K Sengupta No Rating

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 computer exploration (spoilers) possible solution | Comment 1 of 4
`list   10       N=3:PrevN=2   20       while N>=3   30         C=N*PrevN//2-1   40         D=prmdiv(C)   50         C=C//D:Ct=1   60         while C>1   70          DNew=prmdiv(C)   80          if DNew<>D then goto *NotGood   90          C=C//D:inc Ct  100         wend  110         print N,N*PrevN//2-1,D;Ct  120    *NotGood  130         PrevN=N  140         inc N  150       wendOKrun 3       2       2  1 4       5       5  1 5       9       3  2 8       27      3  3Division by zero in 50?n,c 262260          34390022669OK`

The program stopped at N = 262,260, when the combination less 1 became too big (34,390,022,669) for UBASIC to find its lowest prime divisor.

The table is interpreted:

` N   C(N,2)-1   equals 3       2       2^1 4       5       5^1 5       9       3^2 8       27      3^3 `

and no other value of N lower than 262,260 will work.

 Posted by Charlie on 2010-04-18 13:45:26

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