Let $z$ be a complex number, and let $n$ be a positive integer such that $z^n = (z + 1)^n = 1$. Prove that $n$ is divisible by 6.
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
125855
Prove: The product of any three consecutive integers is divisible by $6$.
158524
Complex numbers $z$ such that $|z|= 1$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
150007
Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group.
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
108746
Prove that there exist two integers such that i - j is divisible by n.
280
Prove by induction that $5^n - 1$ is divisible by $4$.
46701
Complex Number Proof Questions
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
91921
Divisibility of $n\cdot2^n+1$ by 3.
105854
Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
113993
Complex power of a complex number
140968
Proof for Property of Complex Numbers
136367
Prove $ ∀a, b, c ∈ Z,$ if $ab + ac ≡ 3$ (mod 6) then b $\not\equiv$ c (mod 6).