query: The Solutions $(a,b,c,d)$ of $a^0+a^1+a^2+\cdots+a^{b-1}+a^b=c^d$
positive_passages.docid: 18903
positive_passages.text: Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
negative_passages.docid: 129454
negative_passages.text: Solution to a quadratic form
negative_passages.docid: 116205
negative_passages.text: System of equations in a,b,c,d
negative_passages.docid: 142725
negative_passages.text: The general solution of $x^a = a^x$ for real $a >0$
negative_passages.docid: 33633
negative_passages.text: Re:$ (a,b,c,d)=(pr+qs, qr-ps,pr-qs,ps+qr) $
negative_passages.docid: 61533
negative_passages.text: Solution af a system of 2 quadratic equations
negative_passages.docid: 47737
negative_passages.text: Find all the possible values of $(a,b,c,d)$.
negative_passages.docid: 41689
negative_passages.text: Find all solutions: $x^2 + 2y^2 = z^2$
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 118716
negative_passages.text: If $ABCD$ is a cyclic quadrilateral, then $AC\cdot(AB\cdot BC+CD\cdot DA)=BD\cdot (DA\cdot AB+BC\cdot CD)$
negative_passages.docid: 95669
negative_passages.text: Solutions of $|z| = z^5$ in $\Bbb{C}$?
negative_passages.docid: 106896
negative_passages.text: Number of solutions of $x_1+2x_2+\cdots+kx_k=n$?
negative_passages.docid: 61601
negative_passages.text: How does one derive these solutions to the cubic equation?
negative_passages.docid: 4333
negative_passages.text: Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$
negative_passages.docid: 73079
negative_passages.text: Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
negative_passages.docid: 60902
negative_passages.text: Find general solution for the equation $1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) $
negative_passages.docid: 33314
negative_passages.text: How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?