Answer
a )
1) 3 | (10 - 1) = 3 | 9 >Yes 9 = 3*{3}, 3 $\in$ Z
2) 3 | ( 1 - 10) = 3| -9 >Yes -9 = 3*{-3}, -3 $\in$ Z
3) 3 | (2 - 2) = 3 | 0 >Yes 0 = 3*{0}, 0 $\in$ Z
4) 3 | (8 - 1) = 3| 7 >No 7 ≠ 3*{p} were p $\in$ Z
b) {3,6,9,12,15}
c) {4,7,10,13,16}
d) {5,8,11,14,17}
e)
nT0 > n = 3k, k $\in$ Z
nT1 > n = 3k+1, k $\in$ Z
nT2 > n = 3k+2, k $\in$ Z
Work Step by Step
a )
1) 3 | (10 - 1) = 3 | 9 >Yes 9 = 3*{3}, 3 $\in$ Z
2) 3 | ( 1 - 10) = 3| -9 >Yes -9 = 3*{-3}, -3 $\in$ Z
3) 3 | (2 - 2) = 3 | 0 >Yes 0 = 3*{0}, 0 $\in$ Z
4) 3 | (8 - 1) = 3| 7 >No 7 ≠ 3*{p} were p $\in$ Z
b) {3,6,9,12,15}
c) {4,7,10,13,16}
d) {5,8,11,14,17}
e)
nT0 > n = 3k, k $\in$ Z
nT1 > n = 3k+1, k $\in$ Z
nT2 > n = 3k+2, k $\in$ Z