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I teach math at St. John Fisher College in Rochester.


Apr
13
comment Compound Angles
Is this two separate questions, to compute each of the sine and cosine terms? Or in the problem are the two expressions combined in some expression?
Apr
11
answered G is a finite abelian group
Apr
11
comment G is a finite abelian group
For (i) you need to assume G has even order, since a group of odd order has no elements of order 2 (by Lagrange Theorem).
Apr
7
revised Can every number be written as a small sum of sums of squares?
added 536 characters in body
Apr
7
awarded  Revival
Apr
6
comment Can every number be written as a small sum of sums of squares?
@AlexBecker Yes it is a way large bound. I don't even know how large since I didn't go through the Hua result to see what bound on the number is needed to guarantee 9 or 10 cubes, and then there's the largeness coming from using (1) [the 22s(n) can be gotten from 11 type 2 pyramids I think...]
Apr
6
revised Can every number be written as a small sum of sums of squares?
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Apr
6
answered Can every number be written as a small sum of sums of squares?
Apr
6
comment Help on this divisibility Problem
A bezout proof of gcd(ab,a+b)=1 can be got from ax+by=1. We have (1) (a+b)x + b(y-x) = 1, and (2) (a+b)y + a(x-y) = 1. Now one can multiply the left sides of (1) and (2), and find three of the four terms have (a+b) as a factor and the fourth term has (ab) as a factor, thus getting u,v with (a+b)u + (ab)v = 1.
Apr
6
comment Help on this divisibility Problem
Yes, just thought of that, can use d a prime, as if $ab$ and $a+b$ have no common prime divisor they are coprime.
Apr
6
comment Help on this divisibility Problem
From $d|ab$ and $\gcd(a,b)=1$ doesn't follow $d|a$ or $d|b$ (unless say $d$ is assumed to be prime).
Apr
6
revised Help on this divisibility Problem
edited body
Apr
6
revised Help on this divisibility Problem
added 497 characters in body
Apr
6
awarded  calculus
Apr
6
answered Help on this divisibility Problem
Apr
5
answered Multivariable calculus - Implicit function theorem
Apr
4
comment periodic numbers in every basis
Good. That definition rules out $0.000...$ and makes your argument work (+1).
Apr
4
comment periodic numbers in every basis
Yes. If one allows "ultimately periodic" then rationals are periodic in any base as you say, so the question should require the periodic part begins immediately after the "decimal" point. [However with this definition $0$ would be periodic.]
Apr
4
comment periodic numbers in every basis
Isn't $0.a$ really periodic, as written $0.a0000...$?
Apr
4
comment Calculate angles of a projection of a tetrahedron
You already know all the angles of the projection since it is equilateral, and also the median BD in that case is also the angle bisector (as well as being perpendicular to AC).