Chapter 4: Q34SE (page 307)
Find a set of four mutually relatively prime integers such that no two of them are relatively prime.
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Convert the octal expansion of each of these integers to a
binary expansion.
a) (572)8 b) (1604)8
c) (423)8 d) (2417)8
Show that the hexadecimal expansion of a positive integer can be obtained from its binary expansion by grouping to-gather blocks of four binary digits, adding initial zeros if necessary, and translating each block of four binary digits into a single hexadecimal digit.
Determine whether the integers in each of these sets are Pairwise relatively prime.
a) 21, 34, 55 b) 14, 17, 85
c) 25, 41, 49, 64 d) 17, 18, 19, 23
It can be shown that every integer can be uniquely represented in the form
where, or 1 for j=0,1,2, …., k. Expansions of this type are called balanced ternary expansions. Find the balanced ternary expansions of
a) 5 .
b) 13 .
c) 37 .
d) 79 .
If the product of two integers is 273852711 and their greatestcommon divisor is 23345, what is their least common multiple?
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