Combinatorics | Number Theory

There are five different routes from Tanya's house to the mall and eight routes from the mall to the water park. How many routes are there from Tanya's house to the water park?

Combinatorics | Number Theory

Find the value of n given that 3n permutation 4 = (n-1)permutation 5

Combinatorics | Number Theory

How many 5 letter code words (not necessarily word with sense) can be formed from the letter A B C D E F G H I and J if ? a. The word has at least one vowel

Combinatorics | Number Theory

The six graders at Washington middle school research the history of their city this day still gave a presentation to the other students at the school if they were 64 six skaters list all the ways they could have been divided equally into groups of 10 or fewer students

Combinatorics | Number Theory

6. Find the multiplicative inverse of 8 mod 11 while explaining the algorithm used.

Combinatorics | Number Theory

2. Maya is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use?

Combinatorics | Number Theory

1. Mr.Steve has 120 pastel sticks and 30 pieces of paper to give to his students.
a) Find the largest number of students he can have in his class so that each student gets equal number of pastel sticks and equal number of paper.
b) Briefly explain the technique you used to solve (a).

Combinatorics | Number Theory

Recall that ν(n) is the divisor function and it gives the number of positive divisors of n.
After knowing this, prove that ν(n) is a prime number if and only if n = p^q−1,
where p and q are prime numbers.

Combinatorics | Number Theory

Let a be a positive integer and let p be an odd prime number that does not divide a. Prove that
(a/p) + (2a/p) + (3a/p) + ((p-1)a/p) = 0
We say that (n/p) denotes the Legendre symbol here.

Combinatorics | Number Theory

Does there exist a positive integer n such that n^2 − 71 is evenly divisible by 107? Prove
your assertion.