Combinatorics | Number Theory Answers

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.

Find the value of each of the following quantities:

C(6,1)=

C(8,1)= 

C(10,1)=

Show that the function f:[0,4] by fx=0 where x is rational and fx=2 where x is irrational is not remann integrable but is lesberg integrable

angelie got a high score in her 60 item her score is so close to a perfect score it is divisible by 2 but it leaves 2 remainders when divided by 4?