Homework SourseShow that if a and b are integers such that a 1 and b 1 th
Show that if a and b are integers such that a > 1 and b > 1, then a does not divide ab + 1.
Solution
Statement : if a and b are integers such that a > 1 and b > 1, then a does not divide ab + 1.
Proof :
From this table we can see that there is always reminder 1 because (ab+1)/a = b + 1/a
so this will always give reminder 1.
So if a and b are integers such that a > 1 and b > 1, then a does not divide ab + 1.
| a | b | ab+1 | (ab+1)%a |
| 2 | 2 | 5 | 1 |
| 2 | 3 | 7 | 1 |
| 3 | 2 | 7 | 1 |
| 2 | 4 | 9 | 1 |
| 4 | 2 | 9 | 1 |
| 3 | 4 | 13 | 1 |
| 4 | 3 | 13 | 1 |
| 2 | 5 | 11 | 1 |
| 5 | 2 | 11 | 1 |
