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  • 11 votes cast
Apr
5
awarded  Curious
Apr
4
accepted How to solve a Pell equation using continued fractions
Apr
4
comment How to solve a Pell equation using continued fractions
I see. My program must be wrong. It only gets the correct convergents up until 393/109.
Apr
4
comment How to solve a Pell equation using continued fractions
You're right, my continued fractions are only right up until 393/109.
Apr
4
revised How to solve a Pell equation using continued fractions
[Edit removed during grace period]; added 64 characters in body
Apr
4
revised How to solve a Pell equation using continued fractions
deleted 1 character in body
Apr
4
asked How to solve a Pell equation using continued fractions
Mar
27
accepted First 10 digits of large sum
Mar
27
comment First 10 digits of large sum
I see. Is there any clever way to solve for the first 10 digits? I ended up solving it by writing my own BigInteger class (analogous to java.math.BigInteger). But I was looking for a clever solution!
Mar
27
comment First 10 digits of large sum
Haha, touche. So the carry from the last 38 digits could affect the outcome of the first 10? In fact... the carry from the last N digits could affect the outcome of the first 10, for any N >= 1?
Mar
27
comment First 10 digits of large sum
Thanks. I edited my post to say the first 12 digits.
Mar
27
revised First 10 digits of large sum
edited body
Mar
27
awarded  Commentator
Mar
27
comment First 10 digits of large sum
But your example only has 15 numbers. Is it significant that there are 100 in the Project Euler problem? (As multiplying any number by 100 shifts its digits two places over.)
Mar
27
asked First 10 digits of large sum
Jan
26
asked What can we say about the definite integral and Riemann sums?
Jan
22
comment Prove log(xy) = log x + log y
Right. I just don't see how $\int_{X}^{XY} \frac{dt}{t} = \int_{1}^{Y} \frac{du}{u}$ for your substitution of u.
Jan
22
comment Prove log(xy) = log x + log y
Oh, thanks for reminding me! The chain rule. I see what @columbus8myhw was saying now.
Jan
22
awarded  Critic
Jan
22
comment Prove log(xy) = log x + log y
It almost looks like you are factoring an x out of the integral, and I'm not well-versed enough with calculus to know why this is okay.