Prove $(a+q*d,n) = 1$ where $q$ is the product of all primes which divide n but not a.
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
89175
Proof of $(a+b)^{n+1}$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
140405
Show that there does not exist any $n$ for which $a^n=a$ forall $a\in \Bbb Z_m$ where $m$ is divisible by the square of some prime.
62982
Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
20881
Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
140948
Suppose $p$ and $q$ are odd primes and $p = q + 4a$ for some $a$. Prove that $(\frac ap) = (\frac aq)$ holds.