Asked by Andre
What is the largest integer n such that 1440/(n^2-1) is an integer?
Answers
Answered by
Reiny
factors of 1440
2x720
3x480
4x360
5x288
6x240
8x180
9x160
10x144
12x120
15x96
16x90
18x80
20x72
24x60
30x48
32x45
36x40 ---> that's all of them
values of n^2-1
1,3,8,15,24,35,48,63,80,99,120,143,168,195,288,325,360,399,440,483,529,575,624,675,728
the largest of these that show up in the factor list is 360
and 360 = 19^2 - 1 , where n = 19
2x720
3x480
4x360
5x288
6x240
8x180
9x160
10x144
12x120
15x96
16x90
18x80
20x72
24x60
30x48
32x45
36x40 ---> that's all of them
values of n^2-1
1,3,8,15,24,35,48,63,80,99,120,143,168,195,288,325,360,399,440,483,529,575,624,675,728
the largest of these that show up in the factor list is 360
and 360 = 19^2 - 1 , where n = 19
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