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awarded  Yearling
Jul
23
awarded  Good Answer
Jul
17
comment Alternate solutions to seemingly simple problem
Hint $\ $ Completing a square generalizes to completing a product.
Jul
14
comment Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
The proof is correct. The downvotes are quite puzzling. If you have questions then please feel welcome to ask.
Jul
14
comment Divisibility for 7
@YoTengoUnLCD It is a strong induction with inductive hypothesis: assuming it is true for all polynomials of degree $< n$ we show that it is true for any polynomial of degree $\,n.\ \ $
Jul
12
reviewed Leave Open How to prove that the Fibonacci sequence is periodic mod 5 without using induction?
Jul
12
reviewed Leave Open Prove $\{a(x,y,z)=(ax,y,z)\}$ is a vector space
Jul
12
reviewed Leave Open How can point group symmetry operations be used to reduce the number of independent crystal properties?
Jul
12
reviewed Leave Open Product of all elements in finite group
Jul
12
reviewed Leave Open Any epi with codomain $P$ is split implies $P$ is projective
Jul
12
reviewed Leave Open $n+1$ elements in the free module $R^n$ must be linear dependent?
Jul
10
comment The square roots of different primes are linearly independent over the field of rationals
@Potato fyi: 4 years ago MathJax had many bugs. Tthe typesetting was done by macros composed to workaround these problems,
Jul
9
comment Use Fermat's little theorem to solve $7^{222}$mod $11$
See this answer for proofs of the Congruence Sum, Product, Power and Polynomial Rules.
Jul
8
comment Greatest common divisors equal?
See this answer for a few proofs of this GCD Freshman's Dream.
Jul
8
revised How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
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Jul
8
comment How to remember trig identities?
@StanShunpike This is a special case of series bisection / multisection.
Jul
8
revised Computing the odd terms of the Taylor series of $\frac{z}{e^z-1}$
deleted 101 characters in body
Jul
8
comment Principal ideal domains that are not integral domains
One can find a link to Hungerford's result in the Wikipedia article on principal ideal rings.
Jul
8
comment Simple Linear Diophantine Equation - problem with proof.
@MarkK This can e viewed a bit more conceptually as unique fractionization, and the first part is a special case of the fact that fact that the general solution of an (affine) linear equation is the sum of any particular solution plus the general solution of the associated homogeneous equation
Jul
8
revised Show that if $fd'=f'd $ and the pairs $f, d $ and $f',d' $ are coprime, then $f=f' $ and $d=d' $.
added 113 characters in body