Difference between revisions of "2013 USAJMO Problems/Problem 1"
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| + | ==Problem== | ||
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Are there integers <math> a </math> and <math> b </math> such that <math> a^5b+3 </math> and <math> ab^5+3 </math> are both perfect cubes of integers? | Are there integers <math> a </math> and <math> b </math> such that <math> a^5b+3 </math> and <math> ab^5+3 </math> are both perfect cubes of integers? | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | Consider the equation <math>\bmod 9</math>. | ||
Revision as of 20:30, 11 May 2013
Problem
Are there integers 
and 
such that 
and 
are both perfect cubes of integers?
Solution
Consider the equation 
.
