Let $x$ and $y$ be integers such that $2x+3y$ is a multiple of $17$. Show that $9x+5y$ must also be a multiple of $17$.
118918
Understanding a proof that $2x + 3y$ is divisible by $17$ iff $9x + 5y$ is divisible by $17$
23830
Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
127400
Prove that ∀ n ∈ {n | n ∈ ℕ ∧ n > 7}: n = x*3 + y*5
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
49209
Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
134365
When is this true: If $m^2$ is a multiple of N then m is a multiple of N
11289
Why $d(x) + d(y) \le n$ when proving Mantel's theorem
35066
Nature and number of solutions to $xy=x+y$
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
87994
Find rational points on $x^2 + y^2 = 3$ and on $x^2 + y^2 = 17$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
154944
Quadratic congruence in $ \mathbb{Z}/187\mathbb{Z},\ 187 =11\cdot 17 $
127237
Let $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $5\}$.
147317
multiple choice question on number theory
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5