query: Find the number of integer pairs $x,y$ between $0$ and $100$ such that $x^{20}$ has the same remainder as $y^{50}$ when divided by $101$.
positive_passages.docid: 149841
positive_passages.text: Find the number of integer pairs 0 ≤ a, b ≤ 100 such that a^20 ≡ b^50 (mod 101). Need help with understanding solution
negative_passages.docid: 139173
negative_passages.text: To find last two digits of $2^{100}$
negative_passages.docid: 124295
negative_passages.text: Divison and remainder in Prolog
negative_passages.docid: 148803
negative_passages.text: 501 distinct coprime integers between 1 and 1000?
negative_passages.docid: 12250
negative_passages.text: How to find the prime factorization of $100!$.
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 92700
negative_passages.text: How can I solve $x^2 \equiv 19 \pmod {59}$.
negative_passages.docid: 114262
negative_passages.text: Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
negative_passages.docid: 110460
negative_passages.text: find remainder of a number
negative_passages.docid: 49626
negative_passages.text: Find the last two digits of $33^{100}$
negative_passages.docid: 94700
negative_passages.text: Integer solutions for $x^3+2=y^2$?
negative_passages.docid: 4475
negative_passages.text: Find the remainder when $2^{2016}$ is divided by $47$
negative_passages.docid: 57041
negative_passages.text: How would you prove that $2^{50} < 3^{33}$ without directly calculating the values
negative_passages.docid: 15897
negative_passages.text: Solve a congruence $1978^{20}\equiv x\pmod{125}$
negative_passages.docid: 73160
negative_passages.text: Solving the Diophantine Equation $x^2 - y! = 2001$ and $x^2 - y! = 2016$
negative_passages.docid: 40615
negative_passages.text: Solve for $x$ in the $80^\circ$-$80^\circ$-$20^\circ$ triangle
negative_passages.docid: 66256
negative_passages.text: Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$