Chapter 4: Q46E (page 286)
Show that 1729 is a Carmichael number.
answer is missing in file
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Similarly let n=1729
1729=7X13X19
n-1 is divisible by
Similarly, n-1 is also divisible by
So, n=1729 is a Carmichael number.
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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 .
a) Describe a procedure for finding the prime factorization of an integer.
b) Use this procedure to find the primefactorization of 80,707.
Describe the extended Euclidean algorithm using pseudocode.
Convert (1 1000 0110 0011)2from its binary expansion
to its hexadecimal expansion.
Convert the binary expansion of each of these integers to a decimal expansion.
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