1979 USAMO Problems/Problem 1
Problem
Determine all non-negative integral solutions 
if any, apart from permutations, of the Diophantine Equation 
Solution
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
Recall that 
for all integers 
. Thus the sum we have is anything from 0-14 mod16. But 1599=15mod16, and thus there are no integral solutions to the given Diophantine equation.
See also
| 1979 USAMO (Problems • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
