Solutions to Exercises, Section 3.2
... the base b to be negative, we could only consider values of x that are m rational numbers of the form n , with n an odd number (because bx is not defined for other values of x). The allowable values of y would be hard to describe. Thus this definition would not be useful, and hence logb y is left unde ...
... the base b to be negative, we could only consider values of x that are m rational numbers of the form n , with n an odd number (because bx is not defined for other values of x). The allowable values of y would be hard to describe. Thus this definition would not be useful, and hence logb y is left unde ...
Full text
... is not a happy number if and only if S™(a) = 4 for some m > 0. (See [4] for a proof.) The height of a happy number is the least m > 0 such that 5 ^ ( a ) — 1. Hence, 1 is a happy number of height 0; 10 is a happy number of height 1; and 7 is a happy number, of height 5. Similarly, we define S3 : Z + ...
... is not a happy number if and only if S™(a) = 4 for some m > 0. (See [4] for a proof.) The height of a happy number is the least m > 0 such that 5 ^ ( a ) — 1. Hence, 1 is a happy number of height 0; 10 is a happy number of height 1; and 7 is a happy number, of height 5. Similarly, we define S3 : Z + ...
