Difference between revisions of "2016 UMO Problems/Problem 6"
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==Problem == | ==Problem == | ||
| + | Find all positive integer pairs <math>(u,m)</math> such that <math>u + m^2</math> is divisible by <math>um-1</math>. | ||
== Solution == | == Solution == | ||
| + | |||
| + | <math>(1,2),(1,3),(2,1),(2,2),(2,5),(3,1),(3,5),(5,2),(5,3)</math> | ||
== See Also == | == See Also == | ||
{{UMO box|year=2016|num-b=5|after=Last Question}} | {{UMO box|year=2016|num-b=5|after=Last Question}} | ||
| − | [[Category:]] | + | [[Category: Intermediate Number Theory Problems]] |
such that 
is divisible by 
.
