query: Number theory: find the value of $a$
positive_passages.docid: 152005
positive_passages.text: Given: $\operatorname{gcf}(x,36)=9$ and $\operatorname{lcm}(x,36)=108$. Find $x$.
negative_passages.docid: 41792
negative_passages.text: If $abc=1$, then $\frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $
negative_passages.docid: 74195
negative_passages.text: Find values of $a$ for which function will have real roots
negative_passages.docid: 83662
negative_passages.text: Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
negative_passages.docid: 21986
negative_passages.text: What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?
negative_passages.docid: 14783
negative_passages.text: A Number Theory problem (GCD)
negative_passages.docid: 18964
negative_passages.text: Find the determinant of $I + A$
negative_passages.docid: 20619
negative_passages.text: Finding Rational numbers
negative_passages.docid: 105263
negative_passages.text: Find the value of $x,y$ for the equation $12x+5y=7$ using number theory .
negative_passages.docid: 66892
negative_passages.text: Finding $P$ in $A = P^{-1}JP$ (Jordan Form)
negative_passages.docid: 62959
negative_passages.text: How to find GCD, LCM on a set of numbers
negative_passages.docid: 83307
negative_passages.text: If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
negative_passages.docid: 156032
negative_passages.text: Find a such that $112_a$, $63_a$ and $34_a$ are in an arithmetic progression
negative_passages.docid: 20957
negative_passages.text: If $a+\frac1b=b+\frac1c=c+\frac1a$ for distinct $a$, $b$, $c$, how to find the value of $abc$?
negative_passages.docid: 145617
negative_passages.text: Is there any simple trick to solve the congruence $a^{24}\equiv6a+2\pmod{13}$?
negative_passages.docid: 144148
negative_passages.text: Find the value of $P(1)$
negative_passages.docid: 37603
negative_passages.text: Finding the Integer part of $\sum_{k=2} ^{9999}\frac{1}{\sqrt k}$