query: Show that if p is prime then p not= (a/b)^2 for a and b integers.
positive_passages.docid: 1383
positive_passages.text: How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
negative_passages.docid: 123544
negative_passages.text: Show that $n = 3^{100} + 2$ is not a prime number.
negative_passages.docid: 58114
negative_passages.text: For which primes p is $p^2 + 2$ also prime?
negative_passages.docid: 34588
negative_passages.text: Number Theory: $p!+p=n^2$, $p$ = prime
negative_passages.docid: 130653
negative_passages.text: $p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
negative_passages.docid: 21737
negative_passages.text: If $A|B$ and $B|A$ then prove $A=\pm B$
negative_passages.docid: 78917
negative_passages.text: Show that for any prime numbers $p,q,r$, one has $p^2+q^2 \ne r^2$.
negative_passages.docid: 29251
negative_passages.text: Show that the square of any prime number is the Factof of some integer
negative_passages.docid: 20980
negative_passages.text: Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
negative_passages.docid: 7899
negative_passages.text: Show that if $p$ is prime then $\Bbb Z_p$ is a field
negative_passages.docid: 88036
negative_passages.text: Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
negative_passages.docid: 115758
negative_passages.text: Remainder of division when $p$ is not prime
negative_passages.docid: 143772
negative_passages.text: How can I algebraically prove that $2^n - 1$ is not always prime?
negative_passages.docid: 6700
negative_passages.text: An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
negative_passages.docid: 70463
negative_passages.text: Let $p$ be prime and $a$ be a natural not divisible by $p$. Then, $\exists$ integers $x,y$ such that $ax\equiv y \pmod{p}$ with $0<|x|,|y|<\sqrt{p}$
negative_passages.docid: 30134
negative_passages.text: For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
negative_passages.docid: 72144
negative_passages.text: Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$