Prove that there does not exists RATIONAL numbers $x$ and $y$ such that $x^2 - y^2 = 1002$
74920
Prove that the equation $x^2-y^2 = 2002$ has no integer solution
86893
Show that it is impossible to list the rational numbers in increasing order
85895
Proving all rational numbers including negatives are countable
23301
There does not exist any integer $m$ such that $3n^2+3n+7=m^3$
155112
Are there more rational numbers than integers?
67161
No maximum(minimum) of rationals whose square is lesser(greater) than $2$.
158933
Rational solutions of $y^2 = x^3 - x$
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
95787
Prove or find a counterexample: For all real numbers x and y it holds that x + y is irrational if, and only if, both x and y are irrational.
123544
Show that $n = 3^{100} + 2$ is not a prime number.
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
30478
How to prove that a number is irrational
31744
Proving that there is an irrational number between any two unequal rational numbers.
74229
$2x^2+3y^2=z^2$ does not have a non-zero integral solution.
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
139979
Proof there is a rational between any two reals