0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod 5, 5 mod 7〉 24
mod 35 = 〈4 mod 5, 3 mod 7〉
1 mod 35 = 〈1 mod 5, 1 mod 7〉 13 mod 35 = 〈3 mod 5, 6 mod 7〉 25 mod
35 = 〈0 mod 5, 4 mod 7〉
2 mod 35 = 〈2 mod 5, 2 mod 7〉 14 mod 35 = 〈4 mod 5, 0 mod 7〉...
Lab 7. Boolean Expressions a) Write a program that evaluates the
following expressions. Assign reasonable values to the variables.
Print the results. a<b≥c , √a−7 b2 ≠c , d∨e∧f , a<b∨¬d ∧means
and, ∨means inclusive or, ¬ means not. b) Write a program that asks
a user whether he or she wants to become a Java programmer and
determines if the user typed “yes” (Print true if yes and false
otherwise.) Don't use the if
statement here
a) Use Fermat’s little theorem to compute 52003 mod 7,52003 mod 11, and 52003 mod 13.
b) Use your results from part (a) and the Chinese remaindertheorem to find 52003 mod 1001. (Note that1001 = 7 ⋅ 11 ⋅ 13.)
‘What matters for growth is not so much the rate of investment
but the efficiency with which it is used and the policy environment
in which it takes place.’ Discuss using relevant data and
literature relating to at least two developing countries.
For m, n in Z, define m ~ n if m (mod 7) = n (mod 7).
a. Show that -341 ~ 3194; that is to say 341 is related to 3194
under (mod 7) operation.
b. How many equivalence classes of Z are there under the
relation ~?
c. Pick any class of part (b) and list its first 4 elements.
d. What is the pairwise intersection of the classes of part
(b)?
e. What is the union of...
Use the Chinese remainder theorem. Say that:
x = 6 mod 10
x = 4 mod 9
x = 2 mod 7
Find what is x modulo 10 · 9 ·
7.
Please show all work and the correctness of your analysis.