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Sep
18
comment How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
Nevertheless, it was a valid answer that met the don't exceed $2^{32}$ limit. Thank you.
Sep
18
comment How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
Another blindingly obvious that I missed. Thanks!
Sep
18
accepted How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
Sep
18
comment How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
Aw, now I feel stupid. "How absurdly simple!" as Watson would say.
Sep
18
comment How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
How did you evaluate $\frac{280344576}{3} \equiv 93448192 \pmod{10^9}$
Sep
18
awarded  Editor
Sep
18
revised How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
added 24 characters in body; edited title
Sep
18
comment How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
@HenningMakholm -- I indicated in subject but not in the message; I am only interested in the last nine digits of that expression. I will indicate so in the message as well.
Sep
18
asked How to evaluate last nine digits of $(2^{120} - 1) / 3$ without any intermediate value exceeding $2^{32}$
Feb
22
awarded  Teacher
Nov
26
comment Is the number 100k+11 ever a square?
Correction -- " ... and 89 are squares" should read " ... and 89 can be squares".
Oct
30
comment How can I express the sum of $\sin a+\sin2a+\sin3a+\cdots+\sin(n-1)a$?
@Alex -- The answer posted here is very similar to what Boris Novikov has posted. Look up Telescopic sum
Oct
19
comment Calculate $\sum\limits_{n=1}^\infty (n-1)/10^n$ using pen and paper
You have an Arithmetico Geometric Series.
Oct
19
awarded  Commentator
Oct
19
comment In high school statistics, why does it seem like equations come out of the sky
" They will slaughter us in a nuclear war next week if we don't make our students [memorize a formula] " -- Awesome! :)
Oct
10
comment Solve $4^{9x-4} = 3^{9x-4}$
Try this: Solve for $x$ and $y$ when $p ^ {2x + y} = q ^ {x + y + 1}$ where $p$ and $q$ are two integers that are relatively prime to each other.
Oct
8
comment Fastest way to check if $x^y > y^x$?
Which means one has more permutations to test (I agree that it would still be far more efficient than calculating $x ^ y$ or $y ^ x$.
Oct
8
comment Fastest way to check if $x^y > y^x$?
@Henry -- Did you mean "... 1 and $e$"? When $log$'s operand is less than one, it becomes negative and one has to be careful with inequalities with one side being negative and other being positive.
Oct
5
comment Why does my calculator show $2^{-329} = 0?$
Michael Hardy -- My +1 goes to @AlvinWong whose comment explains why the typical calculator shows zero.
Jul
30
answered What is the meaning of infinitesimal?