Question

Prove that every prime greater than 3 can be written in the form 6n+ 1 or 6n+ 5 for some positive integer n.

Answer #1

Prove that every prime greater than 3 can be written in the form
6n + 1 or 6n + 5 for some positive integer n.

4. Prove that if p is a prime number greater than 3, then p is
of the form 3k + 1 or 3k + 2.
5. Prove that if p is a prime number, then n √p is irrational
for every integer n ≥ 2.
6. Prove or disprove that 3 is the only prime number of the form
n2 −1.
7. Prove that if a is a positive integer of the form 3n+2, then
at least one prime divisor...

Activity 6.6.
(a)
A positive integer that is greater than 11 and not
prime is called composite.
Write a technical definition for the concept of composite number
with a similar level of detail as in the “more complete” definition
of prime number.
Note.
A number is called prime if its only divisors are 1 and
itself.
This definition has some hidden parts: a more complete
definition would be as follows.
A number is called prime if
it is an integer,...

A prime number (or a prime) is an integer greater than
1 that is not a product of two smaller integer. Created a program
on visual studio named PrimeNumberTest that does
the following:
1) prompt the user for input of an integer
2) test if the integer is a prime number
3) display the test result

Prove that every integer of the form 5n + 3 for n ∈ Z, n ≥ 1,
cannot be a perfect square

Prove that if n is a positive integer greater than 1,
then n! + 1 is odd
Prove that if a, b, c are integers such that a2 + b2 =
c2, then at least one of a, b, or c is even.

Let n be an integer greater than 2. Prove that every subgroup of
Dn with odd order is cyclic.

1. The Fundamental Theorem of Arithmetic states: Every integer
greater than or equal to 2 has a unique factorization into prime
integers. Prove by induction the uniqueness part of the Fundamental
Theorem of Arithmetic.

An
integer 'n' greater than 1 is prime if its only positive divisor is
1 or itself. For example, 2, 3, 5, and 7 are prime numbers, but 4,
6, 8, and 9 are not. Write a python program that defines a function
isPrime (number) with the following header: def isPrime (number):
that checks whether a number is prime or not. Use that function in
your main program to count the number of prime numbers that are
less than 5000....

Use strong induction to prove that every natural number n ≥ 2
can be written as n = 2x + 3y, where x and y are integers greater
than or equal to 0. Show the induction step and hypothesis along
with any cases

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