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= | ![]() ![]() ![]() ![]() ![]() ![]() |
(1) |
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= | ![]() ![]() ![]() ![]() |
(2) |
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= | 0.577215... (Euler's constant) | (3) |
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= | 0.422784... = 1 - ![]() |
(4) |
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= | actual/average energy loss | (5) |
Since 2 and 6 hold for arbitrary
c-vectors,
it is clear that
(A) =
(B) and that when y = B(x) one has...
...the Pythagorians knew infinitely many solutions in integers to
a2 + b2 = c2.
That no non-trivial integer solutions exist for
an + bn = cn with integers n > 2 has long
been suspected (Fermat, c.1637). Only during the current decade has this been proved (Wiles, 1995).