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 Single or double (Posted on 2010-12-24)
Both a number N and its half,when augmented by 1 (i.e.N+1 and N/2+1) form a perfect square.
0 is a trivial example.

List 4 more examples.

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 computer solution | Comment 1 of 6
`   10   for I=1 to 10000000   20     Sq1=I*I   30     HalfN=Sq1-1   40     N=2*HalfN   50     Sq2=N+1   60     Sr=int(sqrt(Sq2))   70     if Sr*Sr=Sq2 then print N,N+1;sqrt(N+1),HalfN+1;sqrt(HalfN+1)   80   next`
`finds`
` N              N+1 sqrt(N+1)               (N/2)+1  sqrt((N/2)+1) 0               1  1.0                          1  1.0 48              49  7.0                         25  5.0 1680            1681  41.0                      841  29.0 57120           57121  239.0                    28561  169.0 1940448         1940449  1393.0                 970225  985.0 65918160        65918161  8119.0                32959081  5741.0 2239277040      2239277041  47321.0             1119638521  33461.0 76069501248     76069501249  275807.0           38034750625  195025.0 2584123765440   2584123765441  1607521.0        1292061882721  1136689.0 87784138523760  87784138523761  9369319.0       43892069261881  6625109.0 `

 Posted by Charlie on 2010-12-24 17:29:45

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