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.
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
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Posted by Charlie
on 2010-12-24 17:29:45 |
computer solution
