Let f be the mod-n function for a fixed n. What do the results of Exercises 1 and 2 suggest about the relationship between k • f (a) and f (k • a)?
Exercise 1
If f is the mod-7 function, compute each of the following.
(a) f (752 + 793)
(b) f (752) + f (793)
(c) f (3 • 1759)
(d) 3 • f (1759)
Exercise 2
If f is the mod-12 function, compute each of the following.
(a) f (1259 + 743)
(b) f (1259) + f (743)
(c) f (2 • 319)
(d) 2 • f (319)
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