Advertisements
Advertisements
Question
Find the least positive value of x such that 78 + x ≡ 3 (mod 5)
Sum
Advertisements
Solution
To find the least value of x such that
78 + x ≡ 3 (mod 5)
⇒ 78 + x – 3 = 5n for some integer n.
75 + x = 5n
75 + x is a multiple of 5.
75 + 5 = 80.
80 is a multiple of 5.
Therefore, the least value of x must be 5.
shaalaa.com
Modular Arithmetic
Is there an error in this question or solution?
Chapter 2: Numbers and Sequences - Exercise 2.3 [Page 51]
APPEARS IN
RELATED QUESTIONS
Find the least positive value of x such that 71 ≡ x (mod 8)
Find the least positive value of x such that 96 ≡ `x/7` (mod 5)
Find the least positive value of x such that 5x ≡ 4 (mod 6)
Solve 5x ≡ 4 (mod 6)
Solve 3x – 2 ≡ 0 (mod 11)
What is the time 100 hours after 7 a.m.?
What is time 15 hours before 11 p.m.?
Today is Tuesday. My uncle will come after 45 days. In which day my uncle will be coming?
Find the remainder when 281 is divided by 17.
74k ≡ _____ (mod 100)
