Determine which natural numbers are in the image of f: N x N -> R defined by f(a,b) = (a + 1)(a + 2b) / 2?
But how do I show/prove this??
Favorite Answer
from a = 2 you get the multiples of 3 from
a = 3 the multiples of 4 unfortunately the multiples of 2 aren’t in there so you’ll never get a number with only two as a factor…
so what you need to prove is that x gives you some number and that number + k(x+1)
Also, throw in “the fundamental theorum of algebra”
and I did every combination from 1,1 to 8,10.
List follows, (sorted)
3
5
6
7
9
9
10
11
12
13
14
15
15
15
17
18
18
19
20
21
21
21
22
24
25
26
27
27
28
30
30
30
33
33
34
35
35
36
36
36
36
36
36
36
36
36
36
36
38
39
40
42
42
44
45
45
46
49
50
51
52
55
56
57
60
60
63
63
68
69
70
75
76
77
84
84
91
92
100
108
and unsorted.
113
125
137
149
1511
1613
1715
1817
1919
11021
216
229
2312
2415
2518
2621
2724
2827
2930
21033
3110
3214
3318
3422
3526
3630
3734
3838
3942
31046
4115
4220
4325
4430
4535
4640
4745
4850
4955
41060
5121
5227
5333
5439
5545
5651
5757
5863
5969
51075
6128
6235
6342
6449
6556
6663
6770
6877
6984
61091
7136
7244
7352
7460
7568
7676
7784
7892
79100
710108
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