Fundamental Theorem of Arithmetic
Show that the square root of a prime number is not rational.
Prove: There are infinitely many prime numbers p of the form 4n+3. In other words, show that there exist infinitely many positive integers, n, such that the number 4n+1 is prime.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30. Identify the square numbers that are listed above.
Finding the number of unit digits of a power function.
Find the number of unit digits of 3^100.
What is the value of 1+2+3....+(p-1) (mod p)?
What is the value of 1 + 2 + 3.....+(p-1) (mod p)?
Determining whether or not an expression is multiplicative.
Is this expression multiplicative? Justify your answer. f(n)=1, n>1. Factor n into a product of primes,n=p1^k1* p2^k2... then set f(n)= (-1)^k1+k2+...+kr.
What are the last two digits of ((9)^9)^9?
What are the last two digits of ((9)^9)^9?
Working with congruent and incongruent solutions.
For which integers c, 0<=c<=1001, does the congruence 154x=c(mod1001) have a solution? When there are solutions how many incongruent solutions are there?
Use Fermat's theorem to calculate the remainder when 3^1000 is divided by 7.
Finding integers that do not have primitive roots.
Find all integers larger than 19 and smaller than 31 which do not have primitive roots.
