Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
Advertisement Remove all ads

If x is congruent to 13 modulo 17 then 7x – 3 is congruent to which number modulo 17? - Mathematics

Sum

If x is congruent to 13 modulo 17 then 7x – 3 is congruent to which number modulo 17?

Advertisement Remove all ads

Solution

x ≡ 13 (mod 17)

Let p be the required number   ...(1)

7x – 3 ≡ p (mod 17)   ...(2)

From (1),

x – 13 = 17n for some integer M.

x – 13 is a multiple of 17.

x must be 30.

∴ 30 – 13 = 17

which is a multiple of 17.

From (2),

7 × 30 – 3 ≡ p (mod 17)

210 – 3 ≡ p (mod 17)

207 ≡ p (mod 17)

207 ≡ 3 (mod 17)

∴ P ≡ 3

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 2 Numbers and Sequences
Exercise 2.3 | Q 2 | Page 51
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×