Search & Filtering
Find out if the inverse exists for the following, give reasoning behind your answer. If you conclude that the inverse exists then find the Bezout coefficients and the inverse of the modulo.
(a) 678 modulo 2970
(b) 137 modulo 2350
Find out if the following numbers are prime numbers, show your work:
(a) 773
(b) 733
(c) 377
there are 14 blue and 28 red bulbs to be used for a birthday party. they are to be placed in a plastic bag so that each bag contains the same number. what is the largest plastic bag will be needed
Bazil wrote two numbers in his notebook, {2}^{12}{3}^{2}{5}^{7}{7}^{5} and {2}^{3}{3}^{12}{5}^{2}{7}^{2}. After that he proceeded writing numbers in the notebook according to the following rule. Each time he can write down a positive number equal to the difference of any two numbers already written in the copybook. It is not allowed to repeat the numbers in the notebook. Find the sum of two smallest numbers that can be obtained in the notebook.
Bazil wrote two numbers in his notebook, {2}^{12}{3}^{2}{5}^{7}{7}^{5} and {2}^{3}{3}^{12}{5}^{2}{7}^{2}. After that he proceeded writing numbers in the notebook according to the following rule. Each time he can write down a positive number equal to the difference of any two numbers already written in the copybook. It is not allowed to repeat the numbers in the notebook. Find the sum of two smallest numbers that can be obtained in the notebook.
solve the linear congruence 27x≡6(mod 53)
Bazil wrote two numbers in his notebook, {2}^{12}{3}^{2}{5}^{7}{7}^{5} and {2}^{3}{3}^{12}{5}^{2}{7}^{2}. After that he proceeded writing numbers in the notebook according to the following rule. Each time he can write down a positive number equal to the difference of any two numbers already written in the copybook. It is not allowed to repeat the numbers in the notebook. Find the sum of two smallest numbers that can be obtained in the notebook.
There are 18 boys and 35 girls in a mathematical club. For playing some game, the teacher has to distribute chips among the children (their total number is equal to k, and all of them have to be given). It is necessary that all the boys have the same numbers of chips, all the girls have the same numbers of chips, and each of the children has at least one chip. It has turned out that the teacher can distribute the chips in a single way. Determine the largest possible value of k.
Find the prime factorization of the integers 1234, 10140, and 36000
True or false:
The value of the binomial coefficient "\\displaystyle{{2}\\choose{10}}" is zero.
