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ThudnBlunder
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 Inequality   « on: Jul 13th, 2008, 9:55am » Quote Modify

For any real t > o, define f(t) to be the number of pairs of integers (a,b) which satisfy a2 + b2 < t

Evaluate LIM f(t)/t as t ->
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Obob
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 Re: Inequality   « Reply #1 on: Jul 13th, 2008, 2:25pm » Quote Modify

For large enough t, f(t) is approximately the area of a circle of radius sqrt(t), i.e. pi * t.  So the limit is pi.
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Eigenray
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 Re: Inequality   « Reply #2 on: Jul 13th, 2008, 3:02pm » Quote Modify

Now, to make this "putnam" worthy, how about showing that |f(t) - pi*t| C t23/73
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