Some remarks on Euler`s totient function - HAL
... Clearly α0 . . . αr is k written in binary form. Therefore there can be at most one odd number n such that φ(n) = 2k . If αi = 1 only when Fi is prime, then there exists n odd such that φ(n) = 2k and O(2k ) = 1. On the other hand, if there is an αi such that Fi is not prime, then there does not exis ...
... Clearly α0 . . . αr is k written in binary form. Therefore there can be at most one odd number n such that φ(n) = 2k . If αi = 1 only when Fi is prime, then there exists n odd such that φ(n) = 2k and O(2k ) = 1. On the other hand, if there is an αi such that Fi is not prime, then there does not exis ...
Real Numbers Determine if the number is rational (R) or irrational (I
... Determine if the number is rational (R) or irrational (I). Support your answer: if rational determine if the number is ...
... Determine if the number is rational (R) or irrational (I). Support your answer: if rational determine if the number is ...
Full text
... 1, for any n ≥ 0, the 2n numbers (or words) in Zn are distinct. We now wish to extend this result by finding a condition under which the 2n+1 − 1 numbers (or words) in Z0 ∪ Z1 ∪ · · · ∪ Zn are distinct. Suppose, to the contrary, that there is a least i such that Zi ∩ Zj 6= ∅ for some j > i. Then the ...
... 1, for any n ≥ 0, the 2n numbers (or words) in Zn are distinct. We now wish to extend this result by finding a condition under which the 2n+1 − 1 numbers (or words) in Z0 ∪ Z1 ∪ · · · ∪ Zn are distinct. Suppose, to the contrary, that there is a least i such that Zi ∩ Zj 6= ∅ for some j > i. Then the ...
Calculating Revision
... Use bus stop method to divide including dividing with decimal remainders. ...
... Use bus stop method to divide including dividing with decimal remainders. ...
Lecture slides
... The parity of an integer refers to whether the integer is odd or even - 7 has an odd parity, 42 has an even parity. Theorem: Any two consecutive integers have opposite parity. Outline of proof: Suppose two consecutive integers are given; call them m and m+1. By the parity property , either m is even ...
... The parity of an integer refers to whether the integer is odd or even - 7 has an odd parity, 42 has an even parity. Theorem: Any two consecutive integers have opposite parity. Outline of proof: Suppose two consecutive integers are given; call them m and m+1. By the parity property , either m is even ...
Slide show for UOPX Praxis Workshop 2 at Utah Campus
... Subtract Fractions & Mixed Numbers • Write the two fractions/mixed numbers vertically above each other (lining up place value) • Change the fractions to a common denominator. • Subtract the numerators only (careful to regroup one whole (2/2, 3/3, 4/4, etc.) if you need to borrow). • Put that differ ...
... Subtract Fractions & Mixed Numbers • Write the two fractions/mixed numbers vertically above each other (lining up place value) • Change the fractions to a common denominator. • Subtract the numerators only (careful to regroup one whole (2/2, 3/3, 4/4, etc.) if you need to borrow). • Put that differ ...
Numeracy - Parent Workshop
... demonstrate in class. • Provides an opportunity to collect evidence during practical activities and games. • We use these grids to set individual targets. ...
... demonstrate in class. • Provides an opportunity to collect evidence during practical activities and games. • We use these grids to set individual targets. ...
LarCalc9_ch03_sec1
... Extrema of a Function In calculus, much effort is devoted to determining the behavior of a function f on an interval I. Does f have a maximum value on I? Does it have a minimum value? Where is the function increasing? Where is it decreasing? In this chapter you will learn how derivatives can be use ...
... Extrema of a Function In calculus, much effort is devoted to determining the behavior of a function f on an interval I. Does f have a maximum value on I? Does it have a minimum value? Where is the function increasing? Where is it decreasing? In this chapter you will learn how derivatives can be use ...
