Difference between revisions of "1998 JBMO Problems"
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==Problem 4== | ==Problem 4== | ||
| − | Do there exist 16 three digit numbers, using only three different digits in all, so that the all numbers give different residues when divided by 16? | + | Do[es] there exist 16 three digit numbers, using only three different digits in all, so that the all numbers give different residues when divided by 16? |
[[1998 JBMO Problems/Problem 4|Solution]] | [[1998 JBMO Problems/Problem 4|Solution]] | ||
Latest revision as of 19:10, 31 October 2020
Problem 1
Prove that the number 
(which has 1997 of 1-s and 1998 of 2-s) is a perfect square.
Problem 2
Let 
be a convex pentagon such that 
, 
and 
. Compute the area of the pentagon.
Problem 3
Find all pairs of positive integers 
such that
![\[x^y = y^{x - y}.\]](http://latex.artofproblemsolving.com/9/8/a/98ac839a2ad0030079cd9730649546627b3937a9.png)
Problem 4
Do[es] there exist 16 three digit numbers, using only three different digits in all, so that the all numbers give different residues when divided by 16?
See Also
| 1998 JBMO (Problems • Resources) | ||
| Preceded by 1997 JBMO Problems |
Followed by 1999 JBMO Problems | |
| 1 • 2 • 3 • 4 | ||
| All JBMO Problems and Solutions | ||
