Intereting Posts

Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
Prove equality in triangle inequality for complex numbers
Integral Contest
application of strong vs weak law of large numbers
Finding inverse in non-commutative ring
Why is bounded induction stronger than open induction?
Solving this SDE $dX_t = aX_tdt + bdW_t$, $X_0 = x$ to find $E$
homomorphisms of $C^{\infty}(\mathbb R^{n})$
Is sum of digits of $3^{1000}$ divisible by $7$?
Proving the regular n-gon maximizes area for fixed perimeter.
Is a von Neumann algebra just a C*-algebra which is generated by its projections?
Homotopy equivalent spaces have homotopy equivalent universal covers
Solution for the trigonometric-linear function
Matrix theory textbook recommendation
Relation of the kernels of one bounded operator and its extension

I have this question and I have proved that a/d is congruent to b/d mod(m/d)

However, I don’t know how to go forward to prove a/k is congruent to b/k mod(m/d)

Can anyone help me out? THX

- $n!+1$ being a perfect square
- Proving a set of numbers has arithmetic progressions of arbitrary length, but none infinite
- Find number of integral solutions of $\sqrt{n}+\sqrt{n+7259}$
- Show that $N_n \mid N_m$ if and only if $n \mid m$
- Is there an alternative proof for periodic expansion of decimal fraction?
- Finding integers satisfying $m^2 - n^2 = 1111$

- If a, b ∈ Z are coprime show that 2a + 3b and 3a + 5b are coprime.
- Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
- Which integers can be expressed as a sum of squares of two coprime integers?
- Do Lipschitz/Hurwitz quaternions satisfy the Ore condition?
- Is there a way to determine how many digits a power of 2 will contain?
- Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$
- Prove that $(a-b) \mid (a^n-b^n)$
- Carmichael number factoring
- Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
- $\frac{a^{2}+b^{2}}{1+ab}$ is a perfect square whenever it is an integer

We have $a\equiv b\pmod m\iff a=b+c\cdot m$ where $c$ is some integer

Let $\displaystyle \frac aA=\frac bB=k\implies (A,B)=1$

$\implies k(A-B)=c\cdot m$

Let $(k,m)=D$ and $\displaystyle \frac kK=\frac mM=D\implies (K,M)=1$

$\displaystyle\implies K\cdot D(A-B)=c\cdot M\cdot D\iff K(A-B)=c\cdot M\implies A-B=\frac{c\cdot M}K$

As $(K,M)=1$ and $A-B$ is an integer, $K$ must divide $c,$

$\displaystyle\implies A\equiv B\pmod M\iff \frac ak\equiv \frac bk\pmod {\frac m{(k,m)}}$

as $\displaystyle M=\frac mD=\frac m{(k,m)}$

- Periodic solution of differential equation y′=f(y)
- Product of all elements in finite group
- Finding the values of $n$ for which $\mathbb{F}_{5^{n}}$, the finite field with $5^{n}$ elements, contains a non-trivial $93$rd root of unity
- Prove the centralizer of an element in group $G$ is a subgroup of $G$
- I want to get good at math, any good book suggestions?
- What's a proof that the angles of a triangle add up to 180°?
- marginal probability mass functions
- Order preserving bijection from $\mathbb Q\times \mathbb Q$ to $\mathbb Q$
- Physicists, not mathematicians, can multiply both sides with $dx$ – why?
- How find this $\lim_{n\to\infty}\sum_{i=1}^{n}\left(\frac{i}{n}\right)^n$
- Do commuting matrices share the same eigenvectors?
- determining an integral using only derivative properties of two functions
- Independence of $H(f)=\int_M \alpha \wedge f^* \beta$ on choice of $d\alpha=f^*\beta$?
- The Blind Man and Coins Puzzle
- Graph Theory Path Problem