2015 UNCO Math Contest II Problems/Problem 6
Problem
How many ordered pairs of positive integers satisfying have the property that their product is less than ?
Solution
We can check every possible case by considering m = 1 and n = 2 through 50, m = 2 and n = 3 through 50, etc. Note that whereby it is obvious that for m = 1 through 40, all possible n work. This accounts for cases. We individually check the remaining cases. Note that and so m = 41 contributes cases. Similarly, m = 42 contributes 5 cases, m = 43 contributes 3 cases, and m = 44 contributes 1 case. This sums to .
See also
2015 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |