### Answers (45)

 203 How can you prove that $1+ 5+ 9 + \cdots +(4n-3) = 2n^{2} - n$ without using induction? 11 How to find the value of an unknown exponent? 10 A condition for being a prime: $\;\forall m,n\in\mathbb Z^+\!:\,p=m+n\implies \gcd(m,n)=1$ 9 How to prove that all odd powers of two add one are multiples of three 8 Function that looks a lot like exponential, but isn't

### Reputation (3,063)

 +20 Is “closedness” a proper word? +10 Is there a solution to $2^a+2^b = 10^c+10^d$, with $0 \leq a < b$ and $0 \leq c < d$? +10 Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian. +10 Using a determinant to find the Cartesian equation for a plane from its parametric equations

### Questions (18)

 12 Proof that the Rubik’s Cube group is 2-generated 6 Is there a solution to $2^a+2^b = 10^c+10^d$, with $0 \leq a < b$ and $0 \leq c < d$? 6 Irrationality of $\min$ and $\arg\,\min$ of $\Gamma|_{[1, 2]}$ 5 Probability of making it across a path of $n$ tiles through random walk 5 Why is $S$ specified to be nonempty in Axler’s definition of function spaces $\mathbf F^S$?

### Tags (82)

 208 summation × 4 14 exponentiation × 3 206 induction × 3 12 elementary-set-theory × 4 203 arithmetic-progressions 12 algebra-precalculus × 4 19 exponential-function × 2 12 divisibility × 2 15 combinatorics × 8 12 elementary-number-theory × 2

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 5 Points on a 2D plane spanned by a turtle graphics system

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