Quote:
Originally Posted by sjastro
c^2=a^2+b^2
a^2=c^2-b^2
a^2=(c+b)(c-b)
Hence a^2=(b+c) if (c-b)=1.
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True for all odd integers a>1.
a=2n+1
(for some n in J+)
a^2 = 2n^2+2n+1 = (n^2+n+1) + (n^2+n)
and so
c=n^2+n+1
b=n^2+n
Also true for a=1 if you allow the degenerate triangle (1,1,0).
30+ years since I finished Uni (maths, stats, comp sci)