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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 4: Q1E (page 284)

Show that15is an inverse of7modulo26.

Short Answer

Expert verified

$a b = 15 * 7 = 105 = 26 * 4 + 1 = 1 (mod 26)$

Step by step solution

Step 1

a and b are inverses of each other (mod m) if

$ab = 1 (mod m) a = 15, b = 7, m = 26 a b = 15 * 7 = 105 = 26 * 4 + 1 = 1 (mod 26)$ so, 15

is an inverse of 7(mod 26) .

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Most popular questions from this chapter

39. Show that the integer m with one’s complement representation $(a_{n - 1} a_{n - 2} \dots a_{1} a_{0})$ can be found using the equation $m = - a_{n - 1} (2^{n - 1} - 1) + a_{n - 2} 2^{n - 2} + \dots . + a_{1} \cdot 2 + a_{0}$

Find $210 div 17 and 210 \mod 17$

37. How is the one’s complement representation of the sum of two integers obtained from the one’s complement representations of these integers?

Find four numbers congruent 5modulo 17.

What are the greatest common divisors of these pairs of integers?

$3^{7} \cdot 5^{3} \cdot 7^{3}, 2^{11} \cdot 3^{5} \cdot 5^{9}$
$11 \cdot 13 \cdot 17, 2^{9} \cdot 3^{7} \cdot 5^{5} \cdot 7^{3}$
$23^{31}, 23^{17}$
$41 \cdot 43 \cdot 53, 41 \cdot 43 \cdot 53$
$3^{13} \cdot 5^{17}, 2^{12} \cdot 7^{21}$
$1111, 0$

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Show that15is an inverse of7modulo26.

Short Answer

Step by step solution

Step 1

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Most popular questions from this chapter

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