Number Properties Flashcards
All primes >3 have what property?
Can satisfy 6n+/-1
All primes >2 have what property?
Can satisfy 4n+/-1
If p = sqrt(3x5xk)
And p is an integer - what is k and why)
k=3x5 because it has to be a root of a perfect square
If x+y is even then x-y=?
Even
How do you approach the question:
What is not a prime factor of 2(^16) - 1
2^x -1 is a difference of squares. Solve the equation down to find the prime factors
What is the E/O nature when you add or subtract:
* E O
* E E
* O E
Odd
Even
Odd
Like integers give even
Opposite integers give odd
What impact do exponents have on the even/odd nature of integers?
None unless exponent = 0
When a question asks for the number of prime factors it is asking for what?
The number of distinct prime factors
What is the effect of exponents on the number of prime factors?
x^y has the same number of prime factors as x
(This is not true for all factors)
What is the effect of multiplication on the number of prime factors? x vs Ax
Ax has the same number or more prime factors than x
For a composite number:
N = PF1^a + PF2^b + PF3^c…
What is the total number of factors?
What is the total number of even factors?
- Total number of factors = (a+1)(b+1)(c+1)
- Total number of even factors = (a)(b+1)(c+1)
If the number of prime factors of X is even and X is not prime then X has to be what?
A perfect square
If X is even and X is a prime factor of X then X =?
2
The largest factor of N is?
Itself
For any number N multiplied by and even number, the outcome must be what?
Even
