Difference between revisions of "2021 AIME I Problems/Problem 3"
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==Solution== | ==Solution== | ||
| − | <math>\binom{11}{2} = 55</math> We need to subtract 5 since <math>2^10 - 2^0, 2^1, 2^2, 2^3, 2^4</math> don't work. <math>55-5=\boxed{050}</math> ~hansenhe | + | <math>\binom{11}{2} = 55</math> We need to subtract 5 since <math>2^{10} - 2^0, 2^1, 2^2, 2^3, 2^4</math> don't work. <math>55-5=\boxed{050}</math> ~hansenhe |
==See also== | ==See also== | ||
Revision as of 18:22, 11 March 2021
Problem
Find the number of positive integers less than 
that can be expressed as the difference of two integral powers of 
Solution
We need to subtract 5 since 
don't work. 
~hansenhe
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
