query: Find $ 560^{48} (mod 1001)$?
positive_passages.docid: 360
positive_passages.text: Modular exponentiation by hand ($a^b\bmod c$)
negative_passages.docid: 73025
negative_passages.text: Find min natural number $n$ so that $2^{2002}$ divides $2001^{n}-1$
negative_passages.docid: 30601
negative_passages.text: Number of $60$th primitive roots of $-1$
negative_passages.docid: 36031
negative_passages.text: Finding modular of a fraction
negative_passages.docid: 133430
negative_passages.text: How to solve $x^x=100$?
negative_passages.docid: 90381
negative_passages.text: Concecutive last zeroes in expansion of $100!$
negative_passages.docid: 13317
negative_passages.text: show that $a^{12} \equiv 1 \mod 32760$ for each $a \in \mathbb{Z}$ such that $\text{gcd}(a, 32760) = 1$
negative_passages.docid: 853
negative_passages.text: Write down the sum of sum of  sum of digits of $4444^{4444}$
negative_passages.docid: 114220
negative_passages.text: Find the value of $\large i^{i^{.^{.^.}}}$
negative_passages.docid: 51161
negative_passages.text: Finding the inverse of 84 mod 5
negative_passages.docid: 56463
negative_passages.text: Factorial of a non-integer number
negative_passages.docid: 20504
negative_passages.text: $\forall m,n \in \Bbb N$ : $\ 56786730\mid mn(m^{60}-n^{60})$
negative_passages.docid: 81750
negative_passages.text: $4 \sin 72^\circ \sin 36^\circ = \sqrt 5$
negative_passages.docid: 29298
negative_passages.text: How to calculate modulus of large numbers?
negative_passages.docid: 55049
negative_passages.text: How to find the inverse modulo $m$?
negative_passages.docid: 68960
negative_passages.text: How to solve $ 13x \equiv 1 ~ (\text{mod} ~ 17) $?
negative_passages.docid: 49116
negative_passages.text: Finding the last digit of $103^{103^{103^{103^{103}}}}$