If $x+y+z \equiv 1 \pmod{17}$, where $x,y,z$ are irrationals, then is it true that $x^n + y^n +z^n \equiv 1 \pmod{17}$ for odd $n$?
141371
Prove that $\alpha^n+\beta^n+\gamma^n \equiv 4^n+5^n+(-6)^n \pmod{17}$
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
96535
Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?
26394
Is the sum and difference of two irrationals always irrational?
80658
Prove that the number $19\cdot8^n+17$ is not prime, $n\in\mathbb{Z}^+$
67605
Different proof that $\sqrt{2}$ is irrational
19076
If a.b.c,d are rationals and x is irrational number, then prove that $\frac{ax+b}{cx+d}$ is usually a irrational number. When do exceptions occur?
47232
Prove $\forall a,b,c \in \mathbb Z$, if $ab+ac\equiv 3\pmod 6$ then $b \not\equiv c \pmod 6$ by contraposition
92290
For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$
94983
Can an odd number $n$ divide $2^n-1$?
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
123159
Solutions of the diophantine equation $x+y+z=xyz$?
16548
Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
158368
Irrationals: A Group?