A few days ago
Anonymous

Determine which natural numbers are in the image of f: N x N -> R defined by f(a,b) = (a + 1)(a + 2b) / 2?

Through trying many values, I came to the conclusion that it is all natural numbers that do not belong to 2^n

But how do I show/prove this??

Top 1 Answers
A few days ago
lansingstudent09101

Favorite Answer

Right, I’m thinking that from a = 1 you get the odd numbers

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

0