2. Find 11644 mod 645 Use the following algorithm and show work! procedure modularExponentiation(b: integer, n...
2. Find 11644 mod 645 Use the following algorithm and show work!
procedure modularExponentiation(b: integer, n =
(ak-1ak-2...a1a0)2, m:positive integer)
x:= 1
power := b mod m
for i = 0 to k-1
If ai = 1 then x:= (x⋅power) mod m
power := (power⋅power) mod m
return x ( x equals bn mod m)
Note: in this example m = 645, ai is the binary expansion of 644, b
is 11.
Homework Answers
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2. Find 11644 mod 645 Use the following algorithm and show
work!
procedure modularExponentiation(b: integer, n...
Let m be a positive integer. Show that a mod m - b mod m t...
Let m be a positive integer. Show that a mod m - b mod m t a - b (mod m) Drag the necessary statements and drop them into the appropriate blank to build your proof (mod m Dag the mecesary eemnes a ohem int the approprite Proof method: Proof assumptions), at-qm + Proof by contradiction aaandh mam it Implication(s) and deduction(s) resulting from the assumption(s): a mk + bmk Hqm tr a-(k + q)m+ r Conclusion(s) from implications and...
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8. [10 points) Consider the following algorithm procedure Algorithm(: integer, n: positive integer; 81,...a s integers with vhilei<r print (l, r, mı, arn, 》 if z > am then 1:= m + 1 if za...
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5. (a) Show that 26 = 1 mod 9. (b) Let m be a positive integer,...
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17. Consider the following algorithm: procedure Algorithm(n: positive integer; di,d2.. ,dn: distinct integers) for 1 to n-1 for 1 to n-k if ddi+ then interchange di and di+ print(k, I, d,ddn-1, dn) (a) |3 points Assume that this algorithm receives as input the integer-6 and the corresponding input sequence 41 36 27 31 17 20 Fill out the table below ds (b) 1 point Assume that the algorithm receives the same input values as in part a). Once the algo-...
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Let m be a positive integer. Show that a mod m - b mod m t a - b (mod m) Drag the necessary statements and drop them into the appropriate blank to build your proof (mod m Dag the mecesary eemnes a ohem int the approprite Proof method: Proof assumptions), at-qm + Proof by contradiction aaandh mam it Implication(s) and deduction(s) resulting from the assumption(s): a mk + bmk Hqm tr a-(k + q)m+ r Conclusion(s) from implications and...
8. [10 points) Consider the following algorithm procedure Algorithm(: integer, n: positive integer; 81,...a s integers with vhilei<r print (l, r, mı, arn, 》 if z > am then 1:= m + 1 if za then anstwer-1 return answer 18 and the (a) Assume that this algorithm receives as input the numbersz-32 and corresponding sequence of integers 2 | 3 1 1 4151617| 8| 9 | 10 İ 11 İ 12 | 13 | 14|15 | 16 | 17 |...
5. (a) Show that 26 = 1 mod 9. (b) Let m be a positive integer, and let m = 6q+r where q and r are integers with 0 <r < 6. Use (a) and rules of exponents to show that 2" = 2 mod 9 (c) Use (b) to find an s in {0,1,...,8} with 21024 = s mod 9.
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