Prove by mathematical induction: $x^n - y^n$ is divisible by $x - y$, for all positive integers $n$.
87665
Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
962
divisibility problem using induction
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
122711
Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
153281
Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
8504
Factoring $x^n + y^n$ over the integers
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
80144
Prove that $x-1$ divides $x^n-1$
130093
Prove by Induction : $n < 2^n$
16235
Prove by induction that every positive integer is represented by some binary number?
108698
proof using the mathematical induction