Question

Write out the multiples 3×k modulo 7 for k=1,⋯,7 giving your answers strictly in the range 0≤n<7

Answer 1

The multiples of 3 modulo 7 are 3, 6, 2, 5, 1, 4, 0.

Step-by-step explanation:

The multiples of 3 modulo 7 for k=1 to 7 are:

1. 3 x 1 ≡ 3 (mod 7)
2. 3 x 2 ≡ 6 (mod 7)
3. 3 x 3 ≡ 2 (mod 7)
4. 3 x 4 ≡ 5 (mod 7)
5. 3 x 5 ≡ 1 (mod 7)
6. 3 x 6 ≡ 4 (mod 7)
7. 3 x 7 ≡ 0 (mod 7)

Therefore, the multiples of 3 modulo 7 are: 3, 6, 2, 5, 1, 4, 0.